[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki7\/archives\/4987#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki7\/archives\/4987","headline":"\u30af\u30e9\u30b9 (\u96c6\u5408\u8ad6) – Wikipedia","name":"\u30af\u30e9\u30b9 (\u96c6\u5408\u8ad6) – Wikipedia","description":"\u96c6\u5408\u8ad6\u53ca\u3073\u305d\u306e\u5fdc\u7528\u3068\u3057\u3066\u306e\u6570\u5b66\u306b\u304a\u3051\u308b\u30af\u30e9\u30b9\u307e\u305f\u306f\u985e\uff08\u308b\u3044\u3001\u82f1: class\uff09\u306f\u3001\u96c6\u5408(\u307e\u305f\u306f\u3001\u3057\u3070\u3057\u3070\u5225\u306e\u6570\u5b66\u7684\u5bfe\u8c61)\u306e\u96c6\u307e\u308a\u3067\u3001\u305d\u308c\u306b\u5c5e\u3059\u308b\u5168\u3066\u306e\u5143\u304c\u5171\u901a\u306b\u3082\u3064\u6027\u8cea\u306b\u3088\u3063\u3066\u7d1b\u308c\u306a\u304f\u5b9a\u7fa9\u3055\u308c\u308b\u3082\u306e\u3067\u3042\u308b\u3002\u300c\u30af\u30e9\u30b9\u300d\u306e\u6b63\u78ba\u306a\u5b9a\u7fa9\u306f\u3001\u8b70\u8ad6\u306e\u57fa\u790e\u3068\u306a\u308b\u6587\u8108\u306b\u4f9d\u5b58\u3059\u308b\u3002\u4f8b\u3048\u3070\u3001\u30c4\u30a7\u30eb\u30e1\u30ed\uff1d\u30d5\u30ec\u30f3\u30b1\u30eb\u96c6\u5408\u8ad6 (ZF) \u3067\u306f\u30af\u30e9\u30b9\u306f\u53b3\u5bc6\u306b\u306f\u5b58\u5728\u3057\u306a\u3044\u304c\u3001\u4ed6\u306e\u96c6\u5408\u8ad6\uff08\u305f\u3068\u3048\u3070\u3001\u30ce\u30a4\u30de\u30f3\uff1d\u30d9\u30eb\u30ca\u30a4\u30b9\uff1d\u30b2\u30fc\u30c7\u30eb\u96c6\u5408\u8ad6 (NBG)\uff09\u3067\u306f\u3001\u300c\u30af\u30e9\u30b9\u300d\u306e\u6982\u5ff5\u306f\u516c\u7406\u5316\u3055\u308c\u3066\u3044\u308b\uff08NBG \u306e\u4f8b\u3060\u3068\u3001\u5225\u306e\u91cf (entity) \u306e\u8981\u7d20\u306b\u306a\u3089\u306a\u3044\u3088\u3046\u306a\u91cf\u3068\u3057\u3066\u30af\u30e9\u30b9\u304c\u5b9a\u7fa9\u3055\u308c\u308b\uff09\u3002 \uff08\u3069\u306e\u3088\u3046\u306a\u5b9a\u5f0f\u5316\u3092\u9078\u3093\u3060\u3068\u3057\u3066\u3082\uff09\u300c\u5168\u3066\u306e\u96c6\u5408\u306e\u96c6\u307e\u308a\u300d\u306f\u30af\u30e9\u30b9\u3067\u3042\u308b\u3002\uff08ZF \u3067\u306f\u53b3\u5bc6\u306a\u8a00\u3044\u65b9\u3067\u306f\u306a\u3044\u304c\uff09\u3053\u306e\u30af\u30e9\u30b9\u3060\u304c\u96c6\u5408\u3067\u306a\u3044\u3088\u3046\u306a\u3082\u306e\u306f\u771f\u306e\u30af\u30e9\u30b9 (proper class) 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\u96c6\u5408\u8ad6\u4ee5\u5916\u306e\u6587\u8108\u3067\u306f\u300c\u30af\u30e9\u30b9\u300d\u3092\u300c\u96c6\u5408\u300d\u306e\u540c\u7fa9\u8a9e\u3068\u3057\u3066\u4f7f\u3046\u3053\u3068\u3082\u3042\u308b\u3002\u3053\u306e\u7528\u6cd5\u306f\u30af\u30e9\u30b9\u3068\u96c6\u5408\u304c\u73fe\u4ee3\u7684\u306a\u96c6\u5408\u8ad6\u306e\u7528\u8a9e\u6cd5\u306b\u57fa\u3065\u304f\u533a\u5225\u3092\u3055\u308c\u3066\u3044\u306a\u304b\u3063\u305f\u6642\u4ee3\u304b\u3089\u3042\u308b\u300219\u4e16\u7d00\u4ee5\u524d\u306e\u591a\u304f\u306e”\u30af\u30e9\u30b9”\u306b\u95a2\u3059\u308b\u8b70\u8ad6\u306f\u96c6\u5408\u306e\u3053\u3068\u3092\u6307\u3057\u3066\u3044\u305f\u3001\u3082\u3057\u304f\u306f\u3082\u3063\u3068\u66d6\u6627\u306a\u6982\u5ff5\u3092\u3055\u3057\u3066\u3044\u305f\u3002\u3053\u306e\u610f\u5473\u3067\u306e\u30af\u30e9\u30b9\u306f\u300c\u7d1a\u300d\u3068\u3044\u3046\u8a33\u8a9e\u3092\u5f53\u3066\u308b\u3053\u3068\u304c\u3042\u308b\uff08\u305f\u3068\u3048\u3070\u6ed1\u3089\u304b\u3055\u306e\u30af\u30e9\u30b9\u306e 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class\uff09\u306f\u3001\u96c6\u5408(\u307e\u305f\u306f\u3001\u3057\u3070\u3057\u3070\u5225\u306e\u6570\u5b66\u7684\u5bfe\u8c61)\u306e\u96c6\u307e\u308a\u3067\u3001\u305d\u308c\u306b\u5c5e\u3059\u308b\u5168\u3066\u306e\u5143\u304c\u5171\u901a\u306b\u3082\u3064\u6027\u8cea\u306b\u3088\u3063\u3066\u7d1b\u308c\u306a\u304f\u5b9a\u7fa9\u3055\u308c\u308b\u3082\u306e\u3067\u3042\u308b\u3002\u300c\u30af\u30e9\u30b9\u300d\u306e\u6b63\u78ba\u306a\u5b9a\u7fa9\u306f\u3001\u8b70\u8ad6\u306e\u57fa\u790e\u3068\u306a\u308b\u6587\u8108\u306b\u4f9d\u5b58\u3059\u308b\u3002\u4f8b\u3048\u3070\u3001\u30c4\u30a7\u30eb\u30e1\u30ed\uff1d\u30d5\u30ec\u30f3\u30b1\u30eb\u96c6\u5408\u8ad6 (ZF) \u3067\u306f\u30af\u30e9\u30b9\u306f\u53b3\u5bc6\u306b\u306f\u5b58\u5728\u3057\u306a\u3044\u304c\u3001\u4ed6\u306e\u96c6\u5408\u8ad6\uff08\u305f\u3068\u3048\u3070\u3001\u30ce\u30a4\u30de\u30f3\uff1d\u30d9\u30eb\u30ca\u30a4\u30b9\uff1d\u30b2\u30fc\u30c7\u30eb\u96c6\u5408\u8ad6 (NBG)\uff09\u3067\u306f\u3001\u300c\u30af\u30e9\u30b9\u300d\u306e\u6982\u5ff5\u306f\u516c\u7406\u5316\u3055\u308c\u3066\u3044\u308b\uff08NBG \u306e\u4f8b\u3060\u3068\u3001\u5225\u306e\u91cf (entity) \u306e\u8981\u7d20\u306b\u306a\u3089\u306a\u3044\u3088\u3046\u306a\u91cf\u3068\u3057\u3066\u30af\u30e9\u30b9\u304c\u5b9a\u7fa9\u3055\u308c\u308b\uff09\u3002  \uff08\u3069\u306e\u3088\u3046\u306a\u5b9a\u5f0f\u5316\u3092\u9078\u3093\u3060\u3068\u3057\u3066\u3082\uff09\u300c\u5168\u3066\u306e\u96c6\u5408\u306e\u96c6\u307e\u308a\u300d\u306f\u30af\u30e9\u30b9\u3067\u3042\u308b\u3002\uff08ZF \u3067\u306f\u53b3\u5bc6\u306a\u8a00\u3044\u65b9\u3067\u306f\u306a\u3044\u304c\uff09\u3053\u306e\u30af\u30e9\u30b9\u3060\u304c\u96c6\u5408\u3067\u306a\u3044\u3088\u3046\u306a\u3082\u306e\u306f\u771f\u306e\u30af\u30e9\u30b9 (proper class) \u3068\u547c\u3070\u308c\u3001\u96c6\u5408\u3068\u306a\u308b\u3088\u3046\u306a\u30af\u30e9\u30b9\uff08\u3064\u307e\u308a\u96c6\u5408\uff09\u306f\u5c0f\u3055\u3044\u30af\u30e9\u30b9 (small class) \u3068\u3082\u547c\u3070\u308c\u308b\u3002\u4f8b\u3048\u3070\u3001\u5168\u3066\u306e\u9806\u5e8f\u6570\u304b\u3089\u306a\u308b\u30af\u30e9\u30b9\u3084\u5168\u3066\u306e\u96c6\u5408\u304b\u3089\u306a\u308b\u30af\u30e9\u30b9\u306f\u3001\u591a\u304f\u306e\u5f62\u5f0f\u4f53\u7cfb\u306b\u304a\u3044\u3066\u771f\u306e\u30af\u30e9\u30b9\u3067\u3042\u308b\u3002\u96c6\u5408\u8ad6\u4ee5\u5916\u306e\u6587\u8108\u3067\u306f\u300c\u30af\u30e9\u30b9\u300d\u3092\u300c\u96c6\u5408\u300d\u306e\u540c\u7fa9\u8a9e\u3068\u3057\u3066\u4f7f\u3046\u3053\u3068\u3082\u3042\u308b\u3002\u3053\u306e\u7528\u6cd5\u306f\u30af\u30e9\u30b9\u3068\u96c6\u5408\u304c\u73fe\u4ee3\u7684\u306a\u96c6\u5408\u8ad6\u306e\u7528\u8a9e\u6cd5\u306b\u57fa\u3065\u304f\u533a\u5225\u3092\u3055\u308c\u3066\u3044\u306a\u304b\u3063\u305f\u6642\u4ee3\u304b\u3089\u3042\u308b\u300219\u4e16\u7d00\u4ee5\u524d\u306e\u591a\u304f\u306e”\u30af\u30e9\u30b9”\u306b\u95a2\u3059\u308b\u8b70\u8ad6\u306f\u96c6\u5408\u306e\u3053\u3068\u3092\u6307\u3057\u3066\u3044\u305f\u3001\u3082\u3057\u304f\u306f\u3082\u3063\u3068\u66d6\u6627\u306a\u6982\u5ff5\u3092\u3055\u3057\u3066\u3044\u305f\u3002\u3053\u306e\u610f\u5473\u3067\u306e\u30af\u30e9\u30b9\u306f\u300c\u7d1a\u300d\u3068\u3044\u3046\u8a33\u8a9e\u3092\u5f53\u3066\u308b\u3053\u3068\u304c\u3042\u308b\uff08\u305f\u3068\u3048\u3070\u6ed1\u3089\u304b\u3055\u306e\u30af\u30e9\u30b9\u306e C1-\u7d1a\u306a\u3069\uff09\u3002\u4e0e\u3048\u3089\u308c\u305f\u578b\u306e\u4ee3\u6570\u7684\u5bfe\u8c61\u5168\u3066\u306e\u96c6\u307e\u308a\u306f\u3001\u305f\u3044\u3066\u3044\u771f\u306e\u30af\u30e9\u30b9\u3092\u306a\u3059\u3002\u4f8b\u3048\u3070\u3001\u5168\u3066\u306e\u7fa4\u304b\u3089\u306a\u308b\u30af\u30e9\u30b9\u3001\u5168\u3066\u306e\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u304b\u3089\u306a\u308b\u30af\u30e9\u30b9\u3001\u306a\u3069\u3002\u570f\u8ad6\u3067\u306f\u3001\u5bfe\u8c61\u306e\u96c6\u307e\u308a\u304c\u771f\u30af\u30e9\u30b9\u3092\u306a\u3059\u3082\u306e\uff08\u307e\u305f\u306f\u5c04\u306e\u96c6\u307e\u308a\u304c\u771f\u30af\u30e9\u30b9\u3092\u306a\u3059\u3082\u306e\uff09\u3092\u5927\u304d\u3044\u570f\u3068\u3044\u3046\u3002  \u8d85\u73fe\u5b9f\u6570 (en:Surreal number) \u5168\u4f53\u306f\u3001\u4f53\u306e\u516c\u7406\u3092\u6e80\u305f\u3059\u5bfe\u8c61\u306b\u3088\u308b\u771f\u30af\u30e9\u30b9\u3067\u3042\u308b\u3002\u96c6\u5408\u8ad6\u3067\u306f\u3001\u96c6\u5408\u306e\u96c6\u307e\u308a\u306e\u591a\u304f\u306f\u771f\u30af\u30e9\u30b9\u306b\u306a\u3063\u3066\u3057\u307e\u3046\u3002\u4f8b\u3048\u3070\u3001\u5168\u3066\u306e\u96c6\u5408\u304b\u3089\u306a\u308b\u30af\u30e9\u30b9\u3001\u5168\u3066\u306e\u9806\u5e8f\u6570\u304b\u3089\u306a\u308b\u30af\u30e9\u30b9\u3001\u5168\u3066\u306e\u57fa\u6570\u304b\u3089\u306a\u308b\u30af\u30e9\u30b9\u306a\u3069\u3002\u30af\u30e9\u30b9\u304c\u771f\u30af\u30e9\u30b9\u3067\u3042\u308b\u3053\u3068\u3092\u8a3c\u660e\u3059\u308b\u65b9\u6cd5\u306b\u3001\u5168\u3066\u306e\u9806\u5e8f\u6570\u306b\u3088\u308b\u30af\u30e9\u30b9\u3068\u306e\u9593\u306b\u5168\u5358\u5c04\u3092\u4e0e\u3048\u308b\u3068\u3044\u3046\u3082\u306e\u304c\u3042\u308b\u3002\u3053\u306e\u65b9\u6cd5\u306f\u3001\u4f8b\u3048\u3070\u81ea\u7531\u5b8c\u5099\u675f\u304c\u5b58\u5728\u3057\u306a\u3044\u3053\u3068\u306e\u8a3c\u660e\u306a\u3069\u306b\u4f7f\u308f\u308c\u308b\u3002\u30d1\u30e9\u30c9\u30c3\u30af\u30b9[\u7de8\u96c6]\u30e9\u30c3\u30bb\u30eb\u306e\u30d1\u30e9\u30c9\u30c3\u30af\u30b9\u306a\u3069\u306e\u7d20\u6734\u96c6\u5408\u8ad6\u306e\u30d1\u30e9\u30c9\u30c3\u30af\u30b9\u306f\u300c\u5168\u3066\u306e\u30af\u30e9\u30b9\u304c\u96c6\u5408\u3067\u3042\u308b\u300d\u3068\u3044\u3046\u6b63\u3057\u304f\u306a\u3044\u4eee\u5b9a\u306b\u3088\u3063\u3066\u8aac\u660e\u3055\u308c\u308b\u3002\u53b3\u683c\u306a\u57fa\u790e\u4ed8\u3051\u306e\u4e0b\u3067\u306f\u3001\u3053\u308c\u3089\u306f\u30d1\u30e9\u30c9\u30c3\u30af\u30b9\u306a\u306e\u3067\u306f\u306a\u304f\u3066\u3001\u3042\u308b\u7a2e\u306e\u30af\u30e9\u30b9\u304c\u771f\u30af\u30e9\u30b9\u3067\u3042\u308b\u3053\u3068\u306e\u8a3c\u660e\u3092\u793a\u5506\u3059\u308b\u3082\u306e\u3067\u3042\u308b\u3068\u6349\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u30e9\u30c3\u30bb\u30eb\u306e\u30d1\u30e9\u30c9\u30c3\u30af\u30b9\u306f\u300c\u81ea\u5206\u81ea\u8eab\u306b\u5c5e\u3055\u306a\u3044\u96c6\u5408\u300d\u5168\u4f53\u304c\u771f\u306e\u30af\u30e9\u30b9\u306b\u306a\u308b\u3053\u3068\u3092\u793a\u5506\u3059\u308b\u3057\u3001\u30d6\u30e9\u30ea\uff1d\u30d5\u30a9\u30eb\u30c6\u30a3\u306e\u30d1\u30e9\u30c9\u30c3\u30af\u30b9\u306f\u5168\u3066\u306e\u9806\u5e8f\u6570\u304b\u3089\u306a\u308b\u30af\u30e9\u30b9\u304c\u771f\u306e\u30af\u30e9\u30b9\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u5506\u3057\u3066\u3044\u308b\u3002  \u516c\u7406\u7684\u96c6\u5408\u8ad6\u306b\u304a\u3051\u308b\u30af\u30e9\u30b9[\u7de8\u96c6]ZF\u3067\u306f\u30af\u30e9\u30b9\u306e\u6982\u5ff5\u3092\u5b9a\u5f0f\u5316\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u3044\u306e\u3067\u3001\u30af\u30e9\u30b9\u306f\u30e1\u30bf\u8a00\u8a9e\u306b\u3088\u308b\u540c\u5024\u306a\u8a00\u660e\u3067\u7f6e\u304d\u63db\u3048\u308b\u3053\u3068\u3067\u6271\u3046\u3053\u3068\u306b\u306a\u308b\u3002\u4f8b\u3048\u3070\u3001A{displaystyle {mathcal {A}}} \u3092ZF\u3092\u89e3\u91c8\u3059\u308b\u69cb\u9020\u3068\u3057\u3066\u3001\u30e1\u30bf\u8a00\u8a9e\u3067\u306e\u8868\u73fe {x\u2223x=x}{displaystyle {xmid x=x}} \u306e A{displaystyle {mathcal {A}}} \u306b\u304a\u3051\u308b\u89e3\u91c8\u306f\u3001A{displaystyle {mathcal {A}}} \u306e\u8b70\u8ad6\u9818\u57df\u306b\u5c5e\u3059\u308b\u8981\u7d20\u5168\u3066\u306e\u96c6\u307e\u308a\uff08\u3064\u307e\u308a\u3001A{displaystyle {mathcal {A}}} \u306b\u304a\u3051\u308b\u96c6\u5408\u3059\u3079\u3066\u306e\u96c6\u307e\u308a\uff09\u3067\u3042\u308b\u3002\u3086\u3048\u306b\u3001\u300c\u5168\u3066\u306e\u96c6\u5408\u306e\u6210\u3059\u30af\u30e9\u30b9\u300d\u3092\u8ff0\u8a9e x = x\u3068\uff08\u3042\u308b\u3044\u306f\u305d\u308c\u306b\u540c\u5024\u306a\u8ff0\u8a9e\u3068\uff09\u540c\u4e00\u8996\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002ZF\u96c6\u5408\u8ad6\u3067\u306f\u30af\u30e9\u30b9\u3092\u5f62\u5f0f\u7684\u306b\u6271\u3046\u3053\u3068\u304c\u3067\u304d\u306a\u3044\u306e\u3067\u3001ZF \u306e\u516c\u7406\u7cfb\u3092\u305d\u306e\u307e\u307e\u30af\u30e9\u30b9\u306b\u95a2\u3059\u308b\u8a00\u660e\u306b\u9069\u7528\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u3044\u3002\u3057\u304b\u3057\u3001\u5230\u9054\u4e0d\u80fd\u57fa\u6570 \u03ba \u306e\u5b58\u5728\u3092\u4eee\u5b9a\u3059\u308c\u3070\u300c\u305d\u308c\u3088\u308a\u30e9\u30f3\u30af\u306e\u5c0f\u3055\u306a\u96c6\u5408\u5168\u4f53\u300d\u306f ZF \u306e\u30e2\u30c7\u30eb\uff08\u30b0\u30ed\u30bf\u30f3\u30c7\u30a3\u30fc\u30af\u5b87\u5b99\uff09\u306b\u306a\u308a\u3001\u305d\u306e\u90e8\u5206\u96c6\u5408\u3092\u300c\u30af\u30e9\u30b9\u300d\u3068\u3057\u3066\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u5225\u306a\u65b9\u6cd5\u3068\u3057\u3066\u3001\u30ce\u30a4\u30de\u30f3-\u30d9\u30eb\u30ca\u30a4\u30b9-\u30b2\u30fc\u30c7\u30eb\u306e\u516c\u7406\u7cfb (NBG) \u3092\u4f8b\u306b\u6319\u3052\u3088\u3046\u3002\u3053\u306e\u7406\u8ad6\u3067\u306f\u30af\u30e9\u30b9\u306f\u57fa\u672c\u7684\u306a\u5bfe\u8c61\u3067\u3042\u308a\u3001\u96c6\u5408\u306f\u5225\u306e\u30af\u30e9\u30b9\u306e\u8981\u7d20\u3067\u3042\u308b\u30af\u30e9\u30b9\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u3002\u3057\u304b\u3057\u306a\u304c\u3089\u3001NBG\u306b\u304a\u3051\u308b\u96c6\u5408\u306e\u5b58\u5728\u516c\u7406\u306f\u3001\u30af\u30e9\u30b9\u306e\u4e0a\u3092\u4e98\u308b\u306e\u3067\u306f\u306a\u304f\u3001\u96c6\u5408\u306e\u4e0a\u3092\u4e98\u308b\u91cf\u5316\u306e\u307f\u306b\u5236\u9650\u3055\u308c\u3066\u3044\u308b\u3002\u3053\u308c\u306b\u3088\u308a\u3001NBG \u306f ZF \u306e\u4fdd\u5b58\u62e1\u5927\u3068\u306a\u308b\u3002\u30e2\u30fc\u30b9-\u30b1\u30ea\u30fc\u96c6\u5408\u8ad6 (MK) \u306f\uff08NBG \u306e\u3088\u3046\u306b\uff09\u771f\u30af\u30e9\u30b9\u3092\u57fa\u790e\u7684\u306a\u5bfe\u8c61\u3068\u3057\u3066\u8a8d\u3081\u308b\u3082\u306e\u3060\u304c\u3001\u96c6\u5408\u306e\u5b58\u5728\u516c\u7406\u306e\u4e2d\u3067\u5168\u3066\u306e\u771f\u30af\u30e9\u30b9\u3092\u8d70\u308b\u91cf\u5316\u3092\u3082\u8a31\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001MK\u306fZF\u3084NBG\u3088\u308a\u771f\u306b\u5f37\u3044\u3002\u65b0\u57fa\u790e\u96c6\u5408\u8ad6 (NF) \u3084\u534a\u96c6\u5408\u306e\u7406\u8ad6\u306e\u3088\u3046\u306a\u307b\u304b\u306e\u96c6\u5408\u8ad6\u3067\u3082\u3001\u300c\u771f\u306e\u985e\u300d\u306e\u6982\u5ff5\u306f\u610f\u5473\u3092\u6210\u3059\uff08\u5fc5\u305a\u3057\u3082\u5168\u3066\u306e\u985e\u306f\u96c6\u5408\u3067\u306a\u3044\uff09\u304c\u3001\u96c6\u5408\u6027 (sethood) \u306e\u5224\u5b9a\u898f\u6e96\u304c\u90e8\u5206\u96c6\u5408\u3092\u4f5c\u308b\u64cd\u4f5c\u306e\u4e0b\u3067\u9589\u3058\u3066\u3044\u306a\u3044\u3002\u4f8b\u3048\u3070\u3001\u666e\u904d\u96c6\u5408\u3092\u5099\u3048\u308b\u4efb\u610f\u306e\u96c6\u5408\u8ad6\u306f\u96c6\u5408\u306e\u90e8\u5206\u985e\u3068\u306a\u308b\u3088\u3046\u306a\u771f\u306e\u985e\u3092\u6301\u3064\u3002\u53c2\u8003\u6587\u732e[\u7de8\u96c6]Jech, Thomas (2003), Set Theory, Springer Monographs in Mathematics (third millennium ed.), Berlin, New York: Springer-Verlag, ISBN\u00a0978-3-540-44085-7\u00a0Levy, A. (1979), Basic Set Theory, Berlin, New York: Springer-Verlag\u00a0"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki7\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki7\/archives\/4987#breadcrumbitem","name":"\u30af\u30e9\u30b9 (\u96c6\u5408\u8ad6) – Wikipedia"}}]}]