[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki6\/archives\/9710#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki6\/archives\/9710","headline":"\u30d6\u30e9\u30ea\uff1d\u30d5\u30a9\u30eb\u30c6\u30a3\u306e\u30d1\u30e9\u30c9\u30c3\u30af\u30b9 – Wikipedia","name":"\u30d6\u30e9\u30ea\uff1d\u30d5\u30a9\u30eb\u30c6\u30a3\u306e\u30d1\u30e9\u30c9\u30c3\u30af\u30b9 – Wikipedia","description":"\u30d6\u30e9\u30ea\uff1d\u30d5\u30a9\u30eb\u30c6\u30a3\u306e\u30d1\u30e9\u30c9\u30c3\u30af\u30b9(Burali-Forti paradox)\u3068\u306f\u3001\u6570\u5b66\u306e\u96c6\u5408\u8ad6\u306b\u304a\u3051\u308b\u30d1\u30e9\u30c9\u30c3\u30af\u30b9\u306e\u4e00\u3064\u3067\u3042\u308a\u3001\u300c\u5168\u3066\u306e\u9806\u5e8f\u6570\u306e\u96c6\u5408\u300d\u3068\u3044\u3046\u6982\u5ff5\u3092\u7d20\u6734\u306b\u5c0e\u5165\u3059\u308b\u3068\u77db\u76fe\u304c\u8d77\u3053\u308b\u3068\u3044\u3046\u4e3b\u5f35\u3002\u5373\u3061\u305d\u306e\u3088\u3046\u306a\u5b58\u5728\u3092\u8a31\u3059\u4f53\u7cfb\u306f\u81ea\u5df1\u77db\u76fe\u3057\u3066\u3044\u308b\u3053\u3068\u3092\u793a\u3059\u3002 Table of Contents \u76ee\u6b21\u30d5\u30a9\u30f3\u30fb\u30ce\u30a4\u30de\u30f3\u9806\u5e8f\u6570\u3092\u7528\u3044\u305f\u8aac\u660e[\u7de8\u96c6]\u3088\u308a\u4e00\u822c\u7684\u306a\u8aac\u660e[\u7de8\u96c6]ZFC\u306b\u304a\u3051\u308b\u30d1\u30e9\u30c9\u30c3\u30af\u30b9\u306e\u89e3\u6c7a[\u7de8\u96c6]\u95a2\u9023\u9805\u76ee[\u7de8\u96c6] \u76ee\u6b21 1 \u30d5\u30a9\u30f3\u30fb\u30ce\u30a4\u30de\u30f3\u9806\u5e8f\u6570\u3092\u7528\u3044\u305f\u8aac\u660e 2 \u3088\u308a\u4e00\u822c\u7684\u306a\u8aac\u660e 3 ZFC\u306b\u304a\u3051\u308b\u30d1\u30e9\u30c9\u30c3\u30af\u30b9\u306e\u89e3\u6c7a 4 \u6b74\u53f2 5 \u95a2\u9023\u9805\u76ee 6 \u811a\u6ce8 \u30d5\u30a9\u30f3\u30fb\u30ce\u30a4\u30de\u30f3\u9806\u5e8f\u6570\u3092\u7528\u3044\u305f\u8aac\u660e[\u7de8\u96c6]","datePublished":"2020-05-16","dateModified":"2022-09-14","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki6\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki6\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?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\/11\/book.png","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/24b0d5ca6f381068d756f6337c08e0af9d1eeb6f","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/24b0d5ca6f381068d756f6337c08e0af9d1eeb6f","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/jp\/wiki6\/archives\/9710","about":["Wiki"],"wordCount":1998,"articleBody":"\u30d6\u30e9\u30ea\uff1d\u30d5\u30a9\u30eb\u30c6\u30a3\u306e\u30d1\u30e9\u30c9\u30c3\u30af\u30b9(Burali-Forti paradox)\u3068\u306f\u3001\u6570\u5b66\u306e\u96c6\u5408\u8ad6\u306b\u304a\u3051\u308b\u30d1\u30e9\u30c9\u30c3\u30af\u30b9\u306e\u4e00\u3064\u3067\u3042\u308a\u3001\u300c\u5168\u3066\u306e\u9806\u5e8f\u6570\u306e\u96c6\u5408\u300d\u3068\u3044\u3046\u6982\u5ff5\u3092\u7d20\u6734\u306b\u5c0e\u5165\u3059\u308b\u3068\u77db\u76fe\u304c\u8d77\u3053\u308b\u3068\u3044\u3046\u4e3b\u5f35\u3002\u5373\u3061\u305d\u306e\u3088\u3046\u306a\u5b58\u5728\u3092\u8a31\u3059\u4f53\u7cfb\u306f\u81ea\u5df1\u77db\u76fe\u3057\u3066\u3044\u308b\u3053\u3068\u3092\u793a\u3059\u3002  Table of Contents\u76ee\u6b21\u30d5\u30a9\u30f3\u30fb\u30ce\u30a4\u30de\u30f3\u9806\u5e8f\u6570\u3092\u7528\u3044\u305f\u8aac\u660e[\u7de8\u96c6]\u3088\u308a\u4e00\u822c\u7684\u306a\u8aac\u660e[\u7de8\u96c6]ZFC\u306b\u304a\u3051\u308b\u30d1\u30e9\u30c9\u30c3\u30af\u30b9\u306e\u89e3\u6c7a[\u7de8\u96c6]\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u76ee\u6b21  1 \u30d5\u30a9\u30f3\u30fb\u30ce\u30a4\u30de\u30f3\u9806\u5e8f\u6570\u3092\u7528\u3044\u305f\u8aac\u660e2 \u3088\u308a\u4e00\u822c\u7684\u306a\u8aac\u660e3 ZFC\u306b\u304a\u3051\u308b\u30d1\u30e9\u30c9\u30c3\u30af\u30b9\u306e\u89e3\u6c7a4 \u6b74\u53f25 \u95a2\u9023\u9805\u76ee6 \u811a\u6ce8\u30d5\u30a9\u30f3\u30fb\u30ce\u30a4\u30de\u30f3\u9806\u5e8f\u6570\u3092\u7528\u3044\u305f\u8aac\u660e[\u7de8\u96c6]\u77db\u76fe\u306e\u539f\u56e0\u306f\u3001\u5168\u3066\u306e\u9806\u5e8f\u6570\u306e\u96c6\u5408\u03a9{displaystyle Omega }\u304c\u9806\u5e8f\u6570\u3068\u3057\u3066\u306e\u6027\u8cea\u3092\u5168\u3066\u6e80\u305f\u3059\u304c\u6545\u306b\u3001\u305d\u308c\u81ea\u4f53\u304c\u307e\u305f\u9806\u5e8f\u6570\u3068\u770b\u505a\u3055\u308c\u306d\u3070\u306a\u3089\u306a\u3044\u3053\u3068\u306b\u3042\u308b\u3002\u5f93\u3063\u3066\u3001\u305d\u306e\u5f8c\u7d9a\u9806\u5e8f\u6570\u03a9+1{displaystyle Omega +1}\u3092\u69cb\u6210\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u3053\u308c\u306f\u03a9{displaystyle Omega }\u3088\u308a\u3082\u53b3\u5bc6\u306b\u5927\u304d\u3044\u3002\u3068\u3053\u308d\u304c\u3001\u5b9a\u7fa9\u306b\u3088\u308a\u3053\u306e\u9806\u5e8f\u6570\u3082\u307e\u305f  \u03a9{displaystyle Omega }\u306e\u5143\u3067\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u3002\u3086\u3048\u306b\u03a9\u03a9.{displaystyle Omega {displaystyle alpha }\u3088\u308a\u3082\u5c0f\u3055\u3044\u5168\u3066\u306e\u9806\u5e8f\u6570\u5168\u4f53\u306e\u9806\u5e8f\u578b\u306f\u03b1{displaystyle alpha }\u81ea\u8eab\u3067\u3042\u308b\u3053\u3068\u304c\u5bb9\u6613\u306b\u793a\u3055\u308c\u308b\u3002\u5f93\u3063\u3066\u03a9{displaystyle Omega }\u3088\u308a\u3082\u5c0f\u3055\u3044\u9806\u5e8f\u6570\u5168\u4f53\u306e\u9806\u5e8f\u578b\u306f\u03a9{displaystyle Omega }\u81ea\u8eab\u3067\u3042\u308b\u3002\u4e00\u822c\u306b\u6574\u5217\u96c6\u5408\u306e\u771f\u306e\u5207\u7247((proper initial segment))\u306e\u9806\u5e8f\u578b\u306f\u5168\u4f53\u306e\u9806\u5e8f\u578b\u3088\u308a\u5c0f\u3055\u3044\u3053\u3068\u304c\u5bb9\u6613\u306b\u793a\u3055\u308c\u308b\u3002\u3053\u306e\u3053\u3068\u304b\u3089\u03a9{displaystyle Omega }\u3088\u308a\u5c0f\u3055\u3044\u9806\u5e8f\u6570\u5168\u4f53\u306e\u9806\u5e8f\u578b\u306f\u9806\u5e8f\u6570\u5168\u4f53\u306e\u9806\u5e8f\u578b\u3088\u308a\u5c0f\u3055\u304f\u306a\u304f\u3066\u306f\u306a\u3089\u306a\u3044\u304c\u3001\u3053\u306e\u3053\u3068\u306f\u03a9{displaystyle Omega }\u304c\u03a9{displaystyle Omega }\u3088\u308a\u5c0f\u3055\u3044\u3053\u3068\u3092\u8868\u3057\u3001\u77db\u76fe\u3002\u9806\u5e8f\u6570\u3092\u5168\u3066\u306e\u5148\u884c\u3059\u308b\u9806\u5e8f\u6570\u306e\u96c6\u5408\u3067\u3042\u308b\u3068\u3059\u308b\u30d5\u30a9\u30f3\u30fb\u30ce\u30a4\u30de\u30f3\u306e\u5b9a\u7fa9\u3092\u7528\u3044\u308b\u306a\u3089\u3070\u3001\u3042\u308b\u9806\u5e8f\u6570\u03b1{displaystyle alpha }\u3088\u308a\u3082\u5c0f\u3055\u306a\u5168\u3066\u306e\u9806\u5e8f\u6570\u306e\u9806\u5e8f\u578b\u306f\u03b1{displaystyle alpha }\u81ea\u8eab\u306b\u306a\u308b\u3068\u3044\u3046\u4e3b\u5f35\u306f\u771f\u3067\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u3002\u5f93\u3063\u3066\u30d5\u30a9\u30f3\u30fb\u30ce\u30a4\u30de\u30f3\u9806\u5e8f\u6570\u306e\u300c\u96c6\u307e\u308a\u300d\u306f\u3001\u30e9\u30c3\u30bb\u30eb\u306e\u30d1\u30e9\u30c9\u30c3\u30af\u30b9\u306b\u51fa\u3066\u304f\u308b\u300c\u96c6\u307e\u308a\u300d\u3068\u540c\u69d8\u306b\u3001\u53e4\u5178\u8ad6\u7406\u306b\u3088\u308b\u96c6\u5408\u8ad6\u306b\u304a\u3051\u308b\u300c\u96c6\u5408\u300d\u3068\u898b\u306a\u3059\u3053\u3068\u306f\u3067\u304d\u306a\u3044\u3002\u3057\u304b\u3057NF\u306b\u304a\u3044\u3066\u306f\u3001\u9806\u5e8f\u578b\u306e\u96c6\u307e\u308a(\u6574\u5217\u96c6\u5408\u306e\u9806\u5e8f\u540c\u578b\u306b\u95a2\u3059\u308b\u540c\u5024\u985e\u5168\u4f53)\u306f\u5b9f\u969b\u306b\u96c6\u5408\u3067\u3042\u308a\u3001\u03a9{displaystyle Omega }\u3088\u308a\u3082\u5c0f\u3055\u306a\u9806\u5e8f\u6570\u306e\u9806\u5e8f\u578b\u306f\u5b9f\u306f\u03a9{displaystyle Omega }\u3068\u306f\u7570\u306a\u308b\u3068\u3044\u3046\u5f62\u3067\u30d1\u30e9\u30c9\u30c3\u30af\u30b9\u306f\u56de\u907f\u3055\u308c\u308b\u3002ZFC\u306b\u304a\u3051\u308b\u30d1\u30e9\u30c9\u30c3\u30af\u30b9\u306e\u89e3\u6c7a[\u7de8\u96c6]\u73fe\u4ee3\u7684\u306a\u516c\u7406\u7684\u96c6\u5408\u8ad6\u306b\u304a\u3044\u3066\u306f\u3001\u7121\u5236\u9650\u306a\u5305\u62ec\u539f\u7406\u3001\u3064\u307e\u308a\u300c\u6027\u8ceaP{displaystyle P}\u3092\u6e80\u305f\u3059\u5168\u3066\u306e\u3082\u306e\u306e\u96c6\u5408\u300d\u3068\u3044\u3046\u3088\u3046\u306a\u96c6\u5408\u306e\u69cb\u6210\u3092\u5358\u7d14\u306b\u7981\u6b62\u3059\u308b\u3053\u3068\u3067\u3053\u306e\u77db\u76fe\u3092\u56de\u907f\u3057\u3066\u3044\u308b\u3002\u4f8b\u3048\u3070\u30b4\u30c3\u30c8\u30ed\u30fc\u30d7\u30fb\u30d5\u30ec\u30fc\u30b2\u306e\u516c\u7406\u7cfb\u3067\u306f\u3053\u308c\u306f\u307e\u3060\u7981\u6b62\u3055\u308c\u3066\u3044\u306a\u304b\u3063\u305f\u3002\u306a\u304a\u3001NF\u3067\u306f\u7570\u306a\u3063\u305f\u89e3\u6c7a\u6cd5\u304c\u63a1\u3089\u308c\u3066\u3044\u308b\u3002\u30d6\u30e9\u30ea\uff1d\u30d5\u30a9\u30eb\u30c6\u30a3\u306e\u30d1\u30e9\u30c9\u30c3\u30af\u30b9\u3068\u3044\u3046\u540d\u79f0\u306f1897\u5e74\u306b\u3053\u308c\u3092\u767a\u898b\u3057\u305f\u30c1\u30a7\u30b6\u30fc\u30ec\u30fb\u30d6\u30e9\u30ea\uff1d\u30d5\u30a9\u30eb\u30c6\u30a3\u306b\u7531\u6765\u3059\u308b\u3002\u4f46\u3057\u7570\u8aac\u304c\u3042\u308a\u3001\u30b0\u30ec\u30b4\u30ea\u30fc\u30fb\u30c1\u30e3\u30a4\u30c6\u30a3\u30f3\u306f\u672c\u5f53\u306e\u767a\u898b\u8005\u306f\u30d0\u30fc\u30c8\u30e9\u30f3\u30c9\u30fb\u30e9\u30c3\u30bb\u30eb\u3060\u3068\u8ff0\u3079\u3066\u3044\u308b[1]\u3002\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u30ab\u30f3\u30c8\u30fc\u30eb\u306e\u30d1\u30e9\u30c9\u30c3\u30af\u30b9\u30e9\u30c3\u30bb\u30eb\u306e\u30d1\u30e9\u30c9\u30c3\u30af\u30b9\u30ea\u30b7\u30e3\u30fc\u30eb\u306e\u30d1\u30e9\u30c9\u30c3\u30af\u30b9\u30b8\u30e9\u30fc\u30eb\u306e\u30d1\u30e9\u30c9\u30c3\u30af\u30b9^ Gregory Chaitin. \u201cA Century of Controversy over the Foundations of Mathematics\u201d.   Springer-Verlag. 2008\u5e745\u670822\u65e5\u95b2\u89a7\u3002"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki6\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki6\/archives\/9710#breadcrumbitem","name":"\u30d6\u30e9\u30ea\uff1d\u30d5\u30a9\u30eb\u30c6\u30a3\u306e\u30d1\u30e9\u30c9\u30c3\u30af\u30b9 – Wikipedia"}}]}]