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\u9078\u629e\u516c\u7406\u306f\u901a\u5e38\u3001\u6b21\u306e\u5f62\u5f0f\u3067\u4e0e\u3048\u3089\u308c\u307e\u3059\u3002 \u3059\u3079\u3066\u306e\u5bb6\u65cf\u306e\u305f\u3081\u306b S{displaystyle {mathcal {s}}} \u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u304c\u3042\u308a\u307e\u3059 \u306e {displaystyle v} \uff08SO -Called \u30bb\u30ec\u30af\u30bf \uff09\u3001\u305d\u308c\u306f\u5bb6\u65cf\u306b\u5c5e\u3059\u308b\u5404\u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u304b\u3089\u6b63\u78ba\u306b1\u3064\u306e\u8981\u7d20\u306b\u5c5e\u3057\u307e\u3059 S{displaystyle {mathcal {s}}}  \u2200S{[\u2200X\u2208SX\u2260\u2205]\u2227[\u2200X,Y\u2208S(X\u2260Y\u21d2X\u2229Y=\u2205)]{displaystyle forall _ {mathcal {s}} {big {} {big [} forall _ {xin\u3001{mathcal {s}}} xneq varnothing {big]}\uff01 {big]}} \u21d2\u2203V\u2200X\u2208S\u2203x(X\u2229V={x})}{displaystyle rightArrow\u5b58\u5728_ {v} forall _ {xin\u3001{mathcal {s}}}\u3001\u5b58\u5728_ {x} {big\uff08} xcap v = {x} {big\uff09} {big}}}} \u9078\u629e\u306e\u516c\u7406\u306b\u76f8\u5f53\u3059\u308b\u91cd\u8981\u306a\u30b9\u30c6\u30fc\u30c8\u30e1\u30f3\u30c8\u306b\u306f\u3001\u591a\u6570\u7406\u8ad6\u306e\u6b21\u306e\u7d50\u679c\u304c\u542b\u307e\u308c\u307e\u3059\u3002 TARSKI\u5b9a\u7406\uff1a\u4e0d\u5feb\u306a\u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u306e\u30d5\u30a1\u30df\u30ea\u30fc\u306e\u30c7\u30ab\u30eb\u30c8\u7523\u7269\u306f\u975e\u30ad\u30c3\u30c9\u3067\u3059\u3002 \u4e0d\u5feb\u306a\u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u306e\u30c7\u30ab\u30eb\u30c8\u30d5\u30a1\u30df\u30ea\u30fc\u306e\u7523\u7269\u306e\u8981\u7d20 S= { Si\uff1a \u79c1 \u2208 \u79c1 } {displaystyle {mathcal {s}} = {s_ {i} colon iin i}}} \u3059\u3079\u3066\u306e\u6a5f\u80fd\u304c\u3042\u308a\u307e\u3059 f \uff1a \u79c1 \u2192 \u22c3 Si{displaystyle fcolon ito bigcup s_ {i}} \u72b6\u614b\u3092\u6e80\u305f\u3059 f \uff08 \u79c1 \uff09\uff09 \u2208 Si{s_ {i}}\u306edisplaystyle f\uff08i\uff09} \u3059\u3079\u3066\u306e\u4eba\u306e\u305f\u3081\u306b \u79c1 \u2208 \u79c1 \u3001 {displaystyle iin i\u3001} \u3069\u3053 \u79c1 {displaystyle i} \u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306e\u30bb\u30c3\u30c8\u30bb\u30c3\u30c8\u3067\u3059\u3002 Tarski\u306e\u5b9a\u7406\u306e\u8ad6\u6587\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002\u5c11\u306a\u304f\u3068\u30821\u3064\u306e\u305d\u306e\u3088\u3046\u306a\u6a5f\u80fd\u304c\u3042\u308a\u307e\u3059 f \u3002 {displaystyle f\u3002} Hessenberg\u306e\u5b9a\u7406\uff1a\u5404\u30a8\u30f3\u30c9\u30ec\u30b9\u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u306f\u3001\u305d\u306e\u30c7\u30ab\u30eb\u30c8\u30b9\u30af\u30a8\u30a2\u3001\u3064\u307e\u308a |a |= |a \u00d7 a |\u3002 {displaystyle | a | = | atimes a |\u3002} \u4e09\u5206\u7b4b\u6cd5\uff1a\u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u306e\u5834\u5408 a \u3001 b {displaystyle a\u3001b} \u305d\u308c\u306f\u767a\u751f\u3057\u307e\u3059 |a |= |b |{displaystyle | a | = | b |} \u307e\u305f |B|,}&#8221;>\u307e\u305f |a |< |b |\u3002 {displaystyle | a | ni\u3001 {displaystyle sum {mathfrak {m}} _ {i} X{displaystyle\u3092\u304a\u9858\u3044\u3057\u307e\u3059x} \u8ab0\u3082\u304c\u3001\u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u306e\u30bb\u30c3\u30c8\u3092\u7d42\u3048\u307e\u3057\u305f X.{displaystyle X.} \u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u306e\u9078\u629e\u306e\u516c\u7406 n -\u30a8\u30ec\u30e1\u30f3\u30c8 \uff08 c n \u3001od\u3002 \u6709\u9650\u30bb\u30c3\u30c8\u306e\u305f\u3081\u306e\u9078\u629e\u306e\u516c\u7406 n \u8981\u7d20 \uff09\uff09\u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u3054\u3068\u306b X{displaystyle x} \u305d\u308c\u305e\u308c\u304b\u30891\u3064\u306e\u8981\u7d20\u3092\u9078\u629e\u3059\u308b\u95a2\u6570\u304c\u3042\u308a\u307e\u3059 n{displaystyle n}  &#8211; \u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u306e\u30b5\u30d6\u30bb\u30c3\u30c8\u306e\u8981\u7d20 X.{displaystyle X.} \u8a08\u7b97\u3055\u308c\u305f\u9078\u629e\u516c\u7406 \uff08 CAC \u3001od\u3002 \u9078\u629e\u3057\u305f\u53ef\u7b97\u516c\u7406 \u3001 \u307e\u305f \u3068 \u304a\u304a 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