[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/981#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/981","headline":"\u6587\u306e\u8a00\u8a9e – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2\u3001\u7121\u6599\u200b\u200b\u767e\u79d1\u4e8b\u5178","name":"\u6587\u306e\u8a00\u8a9e – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2\u3001\u7121\u6599\u200b\u200b\u767e\u79d1\u4e8b\u5178","description":"before-content-x4 \u6587\u306e\u8a00\u8a9e – \u4e09\u3064 l = \u27e8 p \u3001 f \u3001 f \u27e9 \u3001 {displaystyle {mathcal {l}} = langle {textbf","datePublished":"2021-06-05","dateModified":"2021-06-05","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/65fc2a0993a80a415db0147bd9c3625924fd00c1","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/65fc2a0993a80a415db0147bd9c3625924fd00c1","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/981","wordCount":20755,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4\u6587\u306e\u8a00\u8a9e – \u4e09\u3064 l = \u27e8 p \u3001 f \u3001 f \u27e9 \u3001 {displaystyle {mathcal {l}} = langle {textbf {p}}\u3001{mathfrak {f}}\u3001varsigma rangle\u3001} \u3069\u3053\uff1a P{displaystyle {textbf {p}}} \u7121\u9650\u306e\u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u3067\u3059\u3001 F{displaystyle {mathfrak {f}}} \u3068\u306e\u53d6\u308a\u5916\u3057\u53ef\u80fd\u306a\u30b3\u30ec\u30af\u30b7\u30e7\u30f3 P{displaystyle {textbf {p}}} f \uff1a F\u2192 N0\u3002 {displaystyle varsigma\uff1a{mathfrak {f}} to mathbb {n} _ {0}\u3002} \u53ce\u96c6\u8981\u7d20 p {displaystyle {textbf {p}}} \u3068\u3044\u3046 \u6587\u306e\u5909\u6570 \u3001\u53ce\u7a6b\u8981\u7d20 f {displaystyle {mathfrak {f}}}  \u63a5\u7d9a\u8a5e \u8a00\u8a9e l \u3001 {displaystyle {mathcal {l}}\u3001} a f {displaystyle varsigma} \u5f7c\u306e \u30b5\u30a4\u30f3 \u3002 \u53ce\u7a6b\u8981\u7d20\u306e\u5b8c\u6210\u3057\u305f\u30b7\u30fc\u30b1\u30f3\u30b9 p \u222a f {displaystyle {textbf {p}} cup {mathfrak {f}}} \u3068\u3044\u3046 \u7891\u6587 \u8a00\u8a9e l \u3002 {displaystyle {mathcal {l}}\u3002}  \u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u306e\u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u304b\u3089\u6700\u5c0f\uff08\u5305\u542b\u306e\u610f\u5473\u3067\uff09 \u3068 {displaystyle y} \u6761\u4ef6\u3092\u6e80\u305f\u3059\uff1a P\u2286Y{displaystyle {textbf {p}} subseteq y} \uff08\u5909\u6570\u3067\u69cb\u6210\u3055\u308c\u308b1\u3064\u306e\u8981\u7d20\u306e\u7891\u6587\u304c\u3042\u308a\u307e\u3059 Y{displaystyle y}   \uff08\u521d\u3081\uff09 f\u03b11\u2026\u03b1\u03c2(f)\u2208Y,\u03b11,\u2026,\u03b1\u03c2(f)\u2208Y,f\u2208F{displaystyle {mathfrak {f}} alpha _ {1} ldots alpha _ {varsigma\uff08{mathfrak {f}}\uff09} in y\u3001quad alpha _ {1}\u3001dots\u3001alpha _ {varsigma\uff08{bidfrak} {fif} {fif} {fif} {fif} {fif} {fif} {fif} {fif} {fif} {fif\uff09 {mathfrak {f}}}  \uff082\uff09 \u3044\u308f\u3086\u308b \u30d5\u30a9\u30fc\u30df\u30e5\u30e9\u306e\u30b3\u30ec\u30af\u30b7\u30e7\u30f3 \u8a00\u8a9e l {displaystyle {mathcal {l}}} \u30b7\u30f3\u30dc\u30eb\u3067\u30de\u30fc\u30af\u3055\u308c\u3066\u3044\u307e\u3059 f r m \uff08 l \uff09\uff09 \u3002 {displaystyle mathbf {frm}\uff08{mathcal {l}}\uff09\u3002}  \u6761\u4ef6\uff081\uff09\u3068\uff082\uff09\u3092\u6e80\u305f\u3059\u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u306f \u8a00\u8a9e\u5f0f\u306e\u69cb\u7bc9\u306b\u9589\u3058\u3089\u308c\u3066\u3044\u307e\u3059 L{displaystyle {mathcal {l}}} \u3002 \u8a00\u3044\u63db\u3048\u308c\u3070\u3001\u30b3\u30ec\u30af\u30b7\u30e7\u30f3 f r m \uff08 l \uff09\uff09 {displaystyle mathbf {frm}\uff08{mathcal {l}}\uff09} \u8a00\u8a9e\u5f0f\u306e\u69cb\u7bc9\u306b\u9589\u3058\u3089\u308c\u3066\u3044\u308b\u5b57\u5e55\u306e\u6700\u5c0f\u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u306f f r m \uff08 l \uff09\uff09 \u3002 {displaystyle mathbf {frm}\uff08{mathcal {l}}\uff09\u3002}  Table of Contents\u53e4\u5178\u7684\u306a\u6587\u7ae0\u306e\u8a00\u8a9e [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] Peana\u7b97\u8853\u8a00\u8a9e [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u820c \u71b1\u306e \u30d4\u30fc\u30ca\u7b97\u8853 [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u820c \u65b9\u5f0f PA\u7b97\u8853 [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30ec\u30f3\u30de\u30c8\uff08\u30d5\u30a9\u30fc\u30df\u30e5\u30e9\u30b7\u30a7\u30a4\u30d7\uff09 [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] lemmat\uff08\u5efa\u8a2d\u306e\u66d6\u6627\u3055\u306b\u3064\u3044\u3066\uff09 [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u4f8b [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u4f8b [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u3044\u304f\u3064\u304b\u306e\u5f0f\u306e\u540c\u6642\u7f6e\u63db [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u4f8b [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u53e4\u5178\u7684\u306a\u6587\u7ae0\u306e\u8a00\u8a9e [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u3055\u305b\u3066 LCIMV= \u27e8 p \u3001 f \u3001 f LK\u27e9 \u3001 {displaystyle {mathcal {l}} _ {mathbf {cimv}} = langle {textbf {p}}\u3001{mathfrak {f}}\u3001varsigma _ {mathbf {lk}} rangle\u3001}        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4 \u3069\u3053 p = { p \u3001 Q \u3001 r \u3001 s \u3001 … } \u3001 {displaystyle mathbf {p} = {mathbf {p}\u3001mathbf {q}\u3001mathbf {r}\u3001mathbf {s}\u3001dots}\u3001}\u3001} f = { c \u3001 a \u3001 k \u3001 n \u3001 \u3068 } {displaystyle {mathfrak {f}} = {mathbf {c}\u3001mathbf {a}\u3001mathbf {k}\u3001mathbf {n}\u3001mathbf {e}}}}}         (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u3068\u3055\u305b\u3066\u304f\u3060\u3055\u3044 f LK\uff08 c \uff09\uff09 = 2 \u3001 f LK\uff08 a \uff09\uff09 = 2 \u3001 f LK\uff08 k \uff09\uff09 = 2 \u3001 f LK\uff08 \u3068 \uff09\uff09 = 2 \u3001 f LK\uff08 n \uff09\uff09 = \u521d\u3081\u3002 {displaystyle varsigma _ {mathbf {lk}}\uff08mathbf {c}\uff09= 2\u3001; varsigma _ {mathbf {lk}}\uff08mathbf {a}\uff09= 2\u3001; varsigma _ {mathbf {lk}}\uff08mathbf {k} {k} = 2\u30012, ^ {k}\uff09 }\uff08mathbf {n}\uff09= 1.}  \u305d\u308c\u304b\u3089 c c n p Q a p Q {displaystyle mathbf {cnplay}}} {cnplay \u8a00\u8a9e\u5f0f\u3067\u3059        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4LCIMV\u3001 {displaystyle {mathcal {l}} _ {mathbf {cimv}}\u3001} \u3057\u304b\u3057 c c n p Q Q a p Q {displaystyle mathbf {cnplay \u79c1 c c n p n a p Q {displaystyle mathbf {ccnpnapq}} \u305d\u3046\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002 Peana\u7b97\u8853\u8a00\u8a9e [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u820c \u71b1\u306e \u30d4\u30fc\u30ca\u7b97\u8853 [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u3055\u305b\u3066 f PA= \u27e8 AMOI2200\u27e9 i niech\u306e = { v0\u3001 v1\u3001 v2\u3001 … } \u3002 {displaystyle varsigma _ {mathbf {p}} = leftlangle {begin {c | c | c} mathbf {a}\uff06mathbf {am}\uff06mathbf {o}\uff06mathbf {i} \\ hline \\ hline \\ line} } _ {0}\u3001mathbf {v} _ {1}\u3001mathbf {v {v}\u3001dos}\u3002}\u3002}\u3002 \u820c LPAt = \u27e8 \u306e \u3001 { a \u3001 m \u3001 o \u3001 \u79c1 } \u3001 f PA\u27e9 {displaystyle {mathcal {l}} _ {mathbf {pa}}^{t} = langle mathbf {v}\u3001{mathbf {a}\u3001mathbf {m}\u3001mathbf {o}\u3001mathbf {i}}\u3001varsigma _ {mathbf} {pa  \u305d\u308c\u306f\u8a00\u8a9e\u3068\u547c\u3070\u308c\u3066\u3044\u307e\u3059 \u71b1\u306e \u30d4\u30fc\u30ca\u7b97\u8853\u3002\u3053\u306e\u8a00\u8a9e\u306e\u5f0f\u304c\u547c\u3070\u308c\u307e\u3059 \u63a2\u7d22 \u30d4\u30fc\u30ca\u7b97\u8853\u3002\u3059\u3079\u3066\u306e\u30d4\u30fc\u30ca\u7b97\u8853\u71b1\u71b1\u71b1\u71b1\u71b1\u306e\u30b3\u30ec\u30af\u30b7\u30e7\u30f3 t r m PA\u3002 {displaystyle mathbf {trm} _ {mathbf {pa}}\u3002}}  \u4fbf\u5229\u306a\u5834\u5408\u3082\u3042\u308a\u307e\u3059 \u306e 0 {displaystyle mathbf {v} _ {0}} \u305d\u308c\u306f\u66f8\u304b\u308c\u3066\u3044\u308b \u30d0\u30c4 \u3001 {displaystyle mathbf {x}\u3001} \u305d\u306e\u4ee3\u308f\u308a \u306e \u521d\u3081 {displaystyle mathbf {v} _ {1}} \u305d\u308c\u306f\u66f8\u304b\u308c\u3066\u3044\u308b \u3068 {displaystyle mathbf {y}} \u4ee3\u308f\u308a\u306b \u306e 2 {displaystyle mathbf {v} _ {2}} \u305d\u308c\u306f\u66f8\u304b\u308c\u3066\u3044\u308b \u3068 \u3002 {displaystyle mathbf {z}\u3002}  \u8a98\u5c0e\u6587\u5b57\u5217\u3092\u5b9a\u7fa9\u3057\u307e\u3059 \u6570\u5b57 \uff1a \u03940\uff1a= o \u3001 \u03941\uff1a= \u79c1 \u3001 \u0394n+1\uff1a= a \u79c1 \u0394n\u3001 n = 0 \u3001 \u521d\u3081 \u3001 2 \u3001 … {displaystyle {boldsymbol {delta}} _ {0}\uff1a= mathbf {o}\u3001quad {boldsymbol {delta}} _ {1}\uff1a= mathbf {i}\u3001quad {boldsymbol {delta}}}} _ {n+1 _ _}}}} Quad N = 0.1,2\u3001\u30c9\u30c3\u30c8} \u820c \u65b9\u5f0f PA\u7b97\u8853 [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u5f0f \u539f\u5b50 Peana Arithmetic\u306f\u6587\u5b57\u5b57\u5e55\u3067\u3059 \u3068 Q t \u521d\u3081 t 2 {displaystyle mathbf {eq} tau _ {1} tau _ {2}} \u3068 l \u305d\u3046\u3067\u3059 t \u521d\u3081 t 2 \u3001 {displaystyle mathbf {le} tau _ {1} tau _ {2}\u3001} \u3069\u3053 t \u521d\u3081 \u3001 t 2 \u2208 t r m p a \u3002 {displaystyle tau _ {1}\u3001tau _ {2} in mathbf {trm} _ {pa}\u3002}  \u306e\u4ee3\u308f\u308a\u306b\u6163\u7fd2\u7684 \u3068 Q t \u521d\u3081 t 2 \u3001 {displaystyle mathbf {eq} tau _ {1} tau _ {2}\u3001} \u305d\u308c\u306f\u66f8\u304b\u308c\u3066\u3044\u308b \uff08 t \u521d\u3081 \u559c\u3093\u3067 t 2 \uff09\uff09 \u3001 {displaystyle\uff08tau _ {1} equiv tau _ {2}\uff09\u3001} \u305d\u306e\u4ee3\u308f\u308a l \u305d\u3046\u3067\u3059 t \u521d\u3081 t 2 \u3001 {displaystyle mathbf {le} tau _ {1} tau _ {2}\u3001} \u305d\u308c\u306f\u66f8\u304b\u308c\u3066\u3044\u308b \uff08 t \u521d\u3081 \u2a7d t 2 \uff09\uff09 \u3002 {displaystyle\uff08tau _ {1} leqslant tau _ {2}\uff09\u3002}  PA\u8a00\u8a9e\u306e\u539f\u5b50\u5f0f\u306e\u30bb\u30c3\u30c8\u3092\u30de\u30fc\u30af\u3057\u307e\u3059 f r m PA\uff08 0 \uff09\uff09 \u3002 {displaystyle mathbf {frm} _ {mathbf {pa}}^{\uff080\uff09}\u3002}  \u4f8b\uff1a PA\u8a00\u8a9e\u306e\u539f\u5b50\u5f0f\u306f\u305d\u3046\u3067\u3059 \u5f0f Peana\u7b97\u8853\u306f\u8a00\u8a9e\u5f0f\u3067\u3059 \u27e8 FrmPA(0)\u3001 { a \u3001 k \u3001 n \u3001 c \u3001 \u3068 } \u222a Q\u2200\u222a Q\u2203\u3001 f KRK\u27e9 \u3001 {displaystyle langle mathbf {frm} _ {mathbf {pa}}^{\uff080\uff09}\u3001{mathbf {a}\u3001mathbf {k}\u3001mathbf {n}\u3001mathbf {c}\u3001mathbf {e}}\u30ab\u30c3\u30d7 \u3069\u3053 Q\u2200 = { \uff08 Q n \u2200 \uff09\uff09 \uff1a n = 0 \u3001 \u521d\u3081 \u3001 2 \u3001 … } \u3001 Q\u2203 = { \uff08 Q n \u2203 \uff09\uff09 \uff1a n = 0 \u3001 \u521d\u3081 \u3001 2 \u3001 … } {displaystyle {mathfrak {Q}}^{forall }={(mathbf {Q} _{n}^{forall }):n=0,1,2,dots },;{mathfrak {Q}}^{exists }={(mathbf {Q} _{n}^{exists }):n=0,1,2,dots }}  \u305d\u3057\u3066\u3001\u3069\u3053 f KRK{displaystyle varsigma _ {mathbf {krk}}} \u7f72\u540d\u3092\u8c4a\u304b\u306b\u3057\u3066\u3044\u307e\u3059 f LK{displaystyle varsigma _ {mathbf {lk}}} \u53ce\u7a6b\u7528 { a \u3001 k \u3001 n \u3001 c \u3001 \u3068 } \u222a Q\u2200 \u222a Q\u2203 \u3001 {displaystyle {mathbf {a}\u3001mathbf {k}\u3001mathbf {n}\u3001mathbf {c}\u3001mathbf {e}}} cup {forall} cup {mathfrak {q}}^{exists}\u3001{exists}\u3001} \u305d\u306e\u305f\u3081 f LK\uff08 Q n \u2200 \uff09\uff09 = f LK\uff08 Q n \u2203 \uff09\uff09 = \u521d\u3081 \u3001 n = 0 \u3001 \u521d\u3081 \u3001 2 \u3001 … {displaystyle varsigma _ {mathbf {lk}}\uff08mathbf {q} _ {n}^{forall}\uff09= varsigma _ {mathbf {lk}}\uff08mathbf {q} _ {n}^{exists}\uff09  \u66f8\u304f\u4ee3\u308f\u308a\u306b \uff08 Q n \u2200 \uff09\uff09 a \u3001 {displaystyle\uff08mathbf {q} _ {n}^{forall}\uff09alpha\u3001} \u901a\u5e38\u306f\u66f8\u304b\u308c\u3066\u3044\u307e\u3059 \uff08 \u2200 \u306e n \uff09\uff09 a \u3001 {displaystyle\uff08forall mathbf {v} _ {n}\uff09alpha\u3001} \u66f8\u304f\u4ee3\u308f\u308a\u306b \uff08 Q n \u2203 \uff09\uff09 a \u3001 {displaystyle\uff08mathbf {q} _ {n}^{exists}\uff09alpha\u3001} \u901a\u5e38\u306f\u66f8\u304b\u308c\u3066\u3044\u307e\u3059 \uff08 \u2203 \u306e n \uff09\uff09 a \u3002 {displaystyle\uff08exists mathbf {v} _ {n}\uff09alpha\u3002}  \u4f8b\uff1a PA\u8a00\u8a9e\u306e\u5f0f\u306f\u305d\u3046\u3067\u3059 E(x\u2a7dy)(\u2203z)(Axz\u2261y){displaystyle mathbf {E} (mathbf {xleqslant y} )(exists mathbf {z} )(mathbf {Axzequiv y} )}C(Axz\u2a7dAyz)(x\u2a7dy){displaystyle mathbf {C} (mathbf {Axzleqslant Ayz} )(mathbf {xleqslant y} )}CN(z\u2261O)C(Mxz\u2a7dMyz)(x\u2a7dy){displaystyle mathbf {CN} (mathbf {zequiv O} )mathbf {C} (mathbf {Mxzleqslant Myz} )(mathbf {xleqslant y} )}\u30ec\u30f3\u30de\u30c8\uff08\u30d5\u30a9\u30fc\u30df\u30e5\u30e9\u30b7\u30a7\u30a4\u30d7\uff09 [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u3055\u305b\u3066 l {displaystyle {mathcal {l}}} \u6587\u8a00\u8a9e\u306b\u306a\u308a\u307e\u3059\u3002 \u6b21\u306b\u3001\u5404\u30d5\u30a9\u30fc\u30df\u30e5\u30e9\u306b\u3064\u3044\u3066 d {displaystyledelta} \u6761\u4ef6\u306e1\u3064\u306f\u3001\u3053\u306e\u8a00\u8a9e\u3067\u767a\u751f\u3057\u307e\u3059 \u03b4\u2208P{discliestyle delta in mathbf {p}}  \uff083\uff09 \u03b4=f\u03b11\u2026\u03b1n{displaystyle delta = {mathfrak {f}} alpha _ {1} ldots alpha _ {n}} \u78ba\u304b\u306b f\u2208F{displaystyle {mathfrak {f}} in {mathfrak {f}}} \u3068 \u03b11,\u2026,\u03b1n\u2208Frm(L){displaystyle alpha _ {1}\u3001dots\u3001alpha _ {n} in mathbf {frm}\uff08{mathcal {l}}\uff09}  \uff084\uff09 \u3053\u306eLemat\u306e\u8a3c\u62e0\u306b\u3064\u3044\u3066\u8003\u616e\u3059\u3079\u304d\u3067\u3059 \u3068 {displaystyle y} \u65b9\u5f0f d {displaystyledelta} \u4e0a\u8a18\u306e\u6761\u4ef6\uff083\uff09\u304a\u3088\u3073\uff084\uff09\u3092\u6e80\u305f\u3057\u3066\u304b\u3089\u3001\u5f0f\u306e\u69cb\u7bc9\u306b\u9589\u3058\u3089\u308c\u3066\u3044\u308b\u3053\u3068\u3092\u793a\u3057\u307e\u3059\u3002 lemmat\uff08\u5efa\u8a2d\u306e\u66d6\u6627\u3055\u306b\u3064\u3044\u3066\uff09 [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u3055\u305b\u3066 l {displaystyle {mathcal {l}}} \u6587\u306e\u8a00\u8a9e\u306b\u306a\u308a\u307e\u3059 a \u521d\u3081 \u3001 … \u3001 a n \u3001 b \u521d\u3081 \u3001 … \u3001 b m {displaystyle alpha _ {1}\u3001dots\u3001alpha _ {n}\u3001beta _ {1}\u3001dots\u3001beta _ {m}} \u305d\u308c\u3089\u306f\u5f0f\u306b\u306a\u308a\u3001\u8a31\u53ef\u3055\u308c\u307e\u3059 f1\u3001 f2\u2208 f {displaystyle {mathfrak {f_ {1}}}\u3001{mathfrak {f_ {2}}} in {mathfrak {f}}}} \u5f7c\u3089\u306f\u305d\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059 f1a \u521d\u3081 … a n = f2b \u521d\u3081 … b m \u3002 {displaystyle {mathfrak {f_ {1}}} alpha _ {1} ldots alpha _ {n} = {mathfrak {f_ {2}}} beta _ {1} ldots beta _ {m}\u3002}}}}  \u305d\u308c\u304b\u3089 f1= f2\u3001 n = m {displaystyle {mathfrak {f_ {1}}} = {mathfrak {f_ {2}}} ,; n = m} \u3068 a \u521d\u3081 = b \u521d\u3081 \u3001 … \u3001 a n = b m \u3002 {displaystyle alpha _ {1} = beta _ {1} ,, dots ,, alpha _ {n} = beta _ {m}\u3002}  Lematics Fr. \u30d5\u30a9\u30fc\u30df\u30e5\u30e9\u5f62\u72b6 \u79c1 \u5efa\u8a2d\u306e\u9732\u51fa\u5ea6 \u6982\u5ff5\u306e\u8a98\u5c0e\u5b9a\u7fa9\u3092\u8a31\u53ef\u3057\u307e\u3059 \u30b5\u30d6\u30d5\u30a9\u30fc\u30e0 \u4e0e\u3048\u3089\u308c\u305f\u5f0f\u3068 \u5909\u6570\u306e\u4ee3\u308f\u308a\u306b\u5225\u306e\u5f0f\u306e\u5f0f\u306e\u7f6e\u63db \uff1a \u30b3\u30ec\u30af\u30b7\u30e7\u30f3 \u30b5\u30d6\u30d5\u30a9\u30fc\u30e0 \u5f0f d {displaystyledelta} \u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u305f\u30bb\u30c3\u30c8\u3092\u547c\u3073\u51fa\u3057\u307e\u3059\u3002 s b f \uff08 d \uff09\uff09 = {\u03b4,je\u015bli\u00a0\u03b4\u2208PSbf(\u03b11)\u222a\u2026\u222aSbf(\u03b1n)\u222a{\u03b4}je\u015bli\u00a0\u03b4=f\u03b11\u2026\u03b1n,f\u2208F.{displaystyle mathbf {sbf}\uff08delta\uff09= {begin {casess} delta\u3001\uff06{mbox {jebox {je\u015bli}} delta in mathbf {p} \\ mathbf {sbf}\uff08alpha _ {1} cup cup mathbf {sbf {sbf {sbf {sbf} cup }\uff06{m box {je\u015bli}} delta = {mathfrak {f}} alpha _ {1} ldots alpha _ {n}\u3001; {mathfrak {f}}\u3002 \u53ef\u5909\u5f0f  d {displaystyledelta} \u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u306e\u8981\u7d20\u3092\u547c\u3073\u51fa\u3057\u307e\u3059 a t \uff08 d \uff09\uff09 = s b f \uff08 d \uff09\uff09 \u2229 p \u3002 {displaystyle mathbf {at}\uff08delta\uff09= mathbf {sbf}\uff08delta\uff09cap mathbf {p}\u3002}  \u4f8b [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] s b f \uff08 c c n p Q a p Q \uff09\uff09 = { p \u3001 Q \u3001 a p Q \u3001 n p \u3001 c n p Q \u3001 c c n p Q a p Q } {displaystyle mathbf {sbf}\uff08mathbf {ccnp}\uff09= {mathbf {sp} {sp} {sp} \u5f0f\u306e\u4ee3\u66ff d {displaystyledelta} \u5f0f \u30d5\u30a1\u30a4 {displaystyle varphi} \u5909\u6570\u306e\u4ee3\u308f\u308a\u306b  s {displaystyleS} \u30d5\u30a9\u30fc\u30df\u30e5\u30e9\u3092\u547c\u3073\u51fa\u3057\u307e\u3059\uff1a \uff08 d \uff09\uff09 [ \u30d5\u30a1\u30a4 \/ s ] = {p,je\u015bli\u00a0p\u2208P\u2216{s}\u03c6je\u015bli\u00a0p=sf(\u03b11[\u03c6\/s])\u2026(\u03b1n[\u03c6\/s])je\u015bli\u00a0\u03b4=f\u03b11\u2026\u03b1n,f\u2208F.{displaystyle\uff08delta\uff09[varphi \/s] = {begin {cases} p\u3001\uff06{mbox {je\u015bli}} pin mathbf {p} setminus {s} \\ varphi\uff06{mbox {je\u015bli}} p = s \\ {fd}\uff08bar \/alpha _ {bid}\uff08baripha _ {1 pha _ {n} [varphi \/s]\uff09\uff06{mbox {je\u015bli}} delta = {mathfrak {f}} alpha _ {1} ldots alpha _ {n}\u3001; {mathfrak {f}} in {mathfrak {f}}}}\u3002 \u305d\u308c\u306f\u767a\u751f\u3057\u307e\u3059 d [ p \/ p ] = d \u3002 {displaystyle delta [p\/p] = delta\u3002} \u3082\u3057\u3082 p \u2209 a t \uff08 d \uff09\uff09 \u3001 {displaystyle pnotin mathbf {at}\uff08delta\uff09\u3001} \u306b d [ \u30d5\u30a1\u30a4 \/ p ] = d \u3002 {displaystyle delta [varphi \/p] = delta\u3002}  \u4f8b [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \uff08 c c n p Q a p Q \uff09\uff09 [ k \u3068 p Q n p \/ Q ] = c c n p k \u3068 p Q n p a p k \u3068 p Q n p {displaysStyle\uff08mathbf {cnpqap}\uff09[mathbf {kepnp} \/mathbf {cnpkep {cnphepmphepmphe \u3044\u304f\u3064\u304b\u306e\u5f0f\u306e\u540c\u6642\u7f6e\u63db [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u591a\u304f\u306e\u5834\u5408\u3001\u30b9\u30ad\u30eb\u306f\u4fbf\u5229\u3067\u3059 \u540c\u6642\u306b \u3044\u304f\u3064\u304b\u306e\u5909\u6570\u306e\u4ee3\u308f\u308a\u306b\u3044\u304f\u3064\u304b\u306e\u5f0f\u306e\u7f6e\u63db\uff1a \u5f0f\u306e\u4ee3\u66ff d {displaystyledelta} \u65b9\u5f0f \u30d5\u30a1\u30a4 1\u3001 … \u3001 \u30d5\u30a1\u30a4 m{displaystyle varphi _ {1}\u3001dots\u3001varphi _ _ {m}} \u5909\u6570\u306e\u4ee3\u308f\u308a\u306b s 1\u3001 … \u3001 s m{displaystyle s_ {1}\u3001dots\u3001s_ {m}} \u30d5\u30a9\u30fc\u30df\u30e5\u30e9\u3092\u547c\u3073\u51fa\u3057\u307e\u3059\uff1a \uff08 d \uff09\uff09 [ \u30d5\u30a1\u30a4 1\/ s 1\u3001 … \u3001 \u30d5\u30a1\u30a4 m\/ s m] = {pje\u015bli\u00a0p\u2208P\u2216{s1,\u2026,sm},\u03c6jje\u015bli\u00a0p=sj,j=1,\u2026,m,f(\u03b11[\u03c61\/s1,\u2026,\u03c6m\/sm])\u2026(\u03b1n[\u03c61\/s1,\u2026,\u03c6m\/sm])je\u015bli\u00a0\u03b4=f\u03b11\u2026\u03b1n,f\u2208F.{displaystyle\uff08delta\uff09[varphi _ {1}\/s_ {1}\u3001dots\u3001varphi _ {m}\/s_ {m}] = {begin {case} {p}\uff06{{mbox {je\u015bli}} {mcodbf {p} setminus {s_ {s_ {s_ {1} {s_ {s_ {s_ {s_ {s_ {s_ {s_ {s_ {s_ {s_ {1} \\ {varphi _ {j}}\uff06{{mbox {je\u015bli}} p = s_ {j} ,, j = 1\u3001dots\u3001m\u3001} \\ {{mathfrak {f}}} \uff09ldots\uff08alpha _ {n} [varphi _ {1}\/s_ {1}\u3001dots\u3001varphi _ {m}\/s_ {m}]}\uff06{{mbox {je\u015bli}} delta = {mathfrak {f}} alpha _ {nd} {n} ld {n} {f}} in {mathfrak {f}}\u3002} end {case}}}} \u4ee3\u66ff\u306e\u7d50\u679c\u306f\u3001\u9806\u5e8f\u306b\u4f9d\u5b58\u3057\u307e\u305b\u3093\u3002 \uff08 d \uff09\uff09 [ \u30d5\u30a1\u30a4 1\/ s 1\u3001 … \u3001 \u30d5\u30a1\u30a4 m\/ s m] = \uff08 d \uff09\uff09 [ \u30d5\u30a1\u30a4 \u03c0(1)\/ s \u03c0(1)\u3001 … \u3001 \u30d5\u30a1\u30a4 \u03c0(m)\/ s \u03c0(m)] {displaystyle\uff08delta\uff09[varphi _ _ {1}\/s_ {1}\u3001dots\u3001varphi _ {m}\/s_ {m}] {pi\uff08m\uff09}]} \u4efb\u610f\u306e\u9806\u5217\u7528 pi {displaystylepi} \u30b3\u30ec\u30af\u30b7\u30e7\u30f3 { \u521d\u3081 \u3001 2 \u3001 … \u3001 n } \u3002 {displaystyle {1,2\u3001dots\u3001n}\u3002}  \u3082\u3057\u3082 p \u3001 Q \u2208 a t \uff08 d \uff09\uff09 {displaytle P\u3001Qin mathbf {at}\uff08\u304b\u3089 \u79c1 Q \u2209 a t \uff08 \u30d5\u30a1\u30a4 \uff09\uff09 \u3001 {discliestyle qnotin mathbf {at}\uff08vk\uff09\u3001} \u306b\uff1a \uff08 d \uff09\uff09 [ \u30d5\u30a1\u30a4 \/ p \u3001 \u03c6 \/ Q ] = (\uff08 d \uff09\uff09 [ \u30d5\u30a1\u30a4 \/ p ] )[ \u03c6 \/ Q ] \u3002 {displaystyle\uff08delta\uff09[valka \/ p\u3001psi \/ q] = {big\uff08}\uff08delta\uff09[vf \/ p] {big\uff09} [psi \/ q]\u3002} \u4f8b [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u6587\u306e\u8a00\u8a9e\u306f\u3001\u304b\u306a\u308a\u91cd\u8981\u306a\u53c2\u7167\u4ee3\u6570\u3092\u8a2d\u5b9a\u3057\u307e\u3059 f \uff1a {displaystyle varsigma {\uff1a}}  \u4ee3\u6570\u5f0f \u8a00\u8a9e l {displaystyle {mathcal {l}}} \u3053\u306e\u8a00\u8a9e\u306e\u7f72\u540d\u306e\u4ee3\u6570\u3092\u547c\u3073\u51fa\u3057\u307e\u3059 AL\u3001 {displaystyle {mathfrak {a}} _ {mathcal {l}}\u3001} \u305d\u306e\u5b87\u5b99\u306f\u305d\u306e\u5b87\u5b99\u3067\u3059 f r m \uff08 l \uff09\uff09 {displaystyle mathbf {frm}\uff08{mathcal {l}}\uff09} \u305d\u3057\u3066\u3069\u306e\u3067 AL\uff08 f\uff09\uff09 \uff08 a 1\u3001 … \u3001 a \u03c2(f)\uff09\uff09 = fa 1… a \u03c2(f)\u3001 dlaf\u2208 F\u3002 {displaystyle {mathfrak {a}} _ {mathcal {l}}\uff08{mathfrak {f}}\uff09\uff08alpha _ {1}\u3001dots\u3001alpha _ {{{mathfrak {f}}}}\uff09 sigma\uff08{mathfrak {f}}\uff09}\u3001qquad {hbox {dla}} ;; {mathfrak {f}} in {mathfrak {f}}\u3002} \u8a00\u8a9e\u4ee3\u6570\u306f\u3001\u7121\u6599\u306e\u4ee3\u6570\u3067\u3059 p {displaystyle mathbf {p}} \u305d\u306e\u7f72\u540d\u306e\u30a2\u30eb\u30b2\u30dc\u30f3\u30af\u30e9\u30b9\u306b\u304a\u3051\u308b\u30d5\u30ea\u30fc\u30b8\u30a7\u30cd\u30ec\u30fc\u30bf\u30fc\u306e\u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u3068\u3057\u3066\uff1a \u4ee3\u6570\u306e\u5834\u5408 C{displaystyle {mathfrak {c}}} \u8a00\u8a9e\u7f72\u540d L{displaystyle {mathcal {l}}} \u305d\u3057\u3066\u3001\u3042\u3089\u3086\u308b\u8907\u88fd v:P\u2192|C|{displaystyle vcolon mathbf {p} to | {mathfrak {c}} |} \u552f\u4e00\u306e\u540c\u6027\u611b\u304c\u3042\u308a\u307e\u3059 AL,v^:AL\u2192C{displaystyle {widehat {{mathfrak {a}} _ {mathcal {l}}\u3001v}} colon {mathfrak {a}} _ {mathcal {l}}} _ { \u62e1\u5927\u3059\u308b v.{displaystyle v\u3002} \u8a00\u8a9e\u304c\u4e0e\u3048\u3089\u308c\u305f\u30b3\u30f3\u30c6\u30ad\u30b9\u30c8\u3067\u78ba\u7acb\u3055\u308c\u305f\u5834\u5408\u3001\u3053\u306e\u540c\u578b\u306f\u30b7\u30f3\u30dc\u30eb\u306b\u3088\u3063\u3066\u5358\u7d14\u306b\u793a\u3055\u308c\u307e\u3059 v^.{displaystyle {widehat {v}}\u3002} \u3054\u4e86\u627f\u304f\u3060\u3055\u3044 \uff08 d \uff09\uff09 [ \u30d5\u30a1\u30a4 \/ s ] = v^\uff08 d \uff09\uff09 \u3001 {displaystyle\uff08delta\uff09[varphi \/s] = {widehat {and}}\uff08delta\uff09\u3001} \u3069\u3053 \u306e \uff1a p \u2192 f r m \uff08 l \uff09\uff09 {displaystyle vcolon mathbf {p} to mathbf {frm}\uff08{mathcal {l}}\uff09} \u30c7\u30fc\u30bf\u306f\u30e2\u30c7\u30eb\u3067\u3059\u3002 \u306e \uff08 p \uff09\uff09 = {\u03c6,p=sp,p\u2208P\u2216{s}.{displaystyle v\uff08p\uff09= {begin {caseses} vph\u3001\uff06p = s \\ p\u3001\uff06pin mathbf {p} setminus {s} .end {caseses}}}} \u3055\u3089\u306b\u3001\u5834\u5408 a t \uff08 d \uff09\uff09 = { s \u521d\u3081 \u3001 … \u3001 s n } {displaystyle mathbf {at}\uff08delta\uff09= {s_ {1}\u3001dots\u3001s_ {n}}}}} \u3068 \u306e \uff1a p \uff1a \u2192 f r m \uff08 l \uff09\uff09 \u3001 {displaystyle V\uff1aMathBf {p}\u30b3\u30ed\u30f3\u304b\u3089MathBf {frm}\uff08{mathcal {l}}\uff09\u3001} \u306b\uff1a v^\uff08 d \uff09\uff09 = \uff08 d \uff09\uff09 [ \u306e \uff08 s 1\uff09\uff09 \/ s 1\u3001 … \u3001 \u306e \uff08 s n\uff09\uff09 \/ s n] \u3002 {displaystyle {widehat {v}}\uff08delta\uff09=\uff08delta\uff09[v\uff08s_ {1}\uff09\/s_ {1}\u3001dots\u3001v\uff08s_ {n}\uff09\/s_ {n}]\u3002}\u3002 \u3055\u305b\u3066 \u30d0\u30c4 {displaystyle x} \u8a00\u8a9e\u5f0f\u306e\u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u306b\u306a\u308a\u307e\u3059 l \u3002 {displaystyle {mathcal {l}}\u3002} \u305d\u308c\u304b\u3089 SbL\uff08 \u30d0\u30c4 \uff09\uff09 = {v^\uff08 d \uff09\uff09 \uff1a d \u2208 \u30d0\u30c4 \u3001 \u306e \uff1a p \u2192 f r m \uff08 L\uff09\uff09 }m repoly ylexted em emb h rbine embook mm ho hol hupe hupe\uff09\uff1amalame mates\uff1a \u4ee3\u66ff\u30eb\u30fc\u30eb \u306e l {displaystyle {mathcal {l}}} \u30eb\u30fc\u30eb\u304c\u3042\u308a\u307e\u3059\uff1a r\u22c6L= {\u27e8{ d } \u3001 v^\uff08 d \uff09\uff09 \u27e9\uff1a d \u2208 \u30d0\u30c4 \u3001 \u306e \uff1a p \u2192 f r m \uff08 L\uff09\uff09 }T\u30ea\u30d7\u30ec\u30a4Ylexted Male Em Hem Hook Mates M Halm M H other M Horm m kupe m kupe kupe kupe qual mupe kmal mm\u3002 \u8a00\u8a9e\u304c\u8a2d\u5b9a\u3055\u308c\u3066\u3044\u308b\u5834\u5408\u3001\u4e0a\u90e8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306f\u898b\u843d\u3068\u3055\u308c\u307e\u3059\u3002 Pogorzelski Witold\u3001 \u6b63\u5f0f\u306a\u8ad6\u7406\u306e\u57fa\u672c\u8f9e\u66f8 \u3001\u7de8\u30ef\u30eb\u30b7\u30e3\u30ef\u5927\u5b66\u306e\u652f\u90e8\u3001\u30d3\u30a2\u30a6\u30a3\u30b9\u30c8\u30af1992\u3002 Pogorzelski Witold\u3001 \u53e4\u5178\u7684\u306a\u6587\u306e\u30a2\u30ab\u30a6\u30f3\u30c8 \u3001\u30ef\u30eb\u30b7\u30e3\u30ef1975\u3002 \u30cf\u30f3\u30bf\u30fc\u30b8\u30a7\u30d5\u30ea\u30fc\u3001 Metalogika \u3001\u30ef\u30eb\u30b7\u30e3\u30ef\u3001PWN 1982\u3002 Shoenfield Joseph R.\u3001 \u6570\u5b66\u7684\u8ad6\u7406 \u3001Addison-Wesley\u30011967\u5e74\u3002      (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/981#breadcrumbitem","name":"\u6587\u306e\u8a00\u8a9e – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2\u3001\u7121\u6599\u200b\u200b\u767e\u79d1\u4e8b\u5178"}}]}]