{"id":52627,"date":"2024-06-09T07:00:57","date_gmt":"2024-06-09T07:00:57","guid":{"rendered":"https:\/\/science-hub.click\/%E3%83%9A%E3%82%A2%E3%83%8E%E3%81%AE%E5%85%AC%E7%90%86%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A9%B3%E3%81%97%E3%81%8F%E8%A7%A3%E8%AA%AC\/"},"modified":"2024-06-09T07:00:57","modified_gmt":"2024-06-09T07:00:57","slug":"%E3%83%9A%E3%82%A2%E3%83%8E%E3%81%AE%E5%85%AC%E7%90%86%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A9%B3%E3%81%97%E3%81%8F%E8%A7%A3%E8%AA%AC","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=52627","title":{"rendered":"\u30da\u30a2\u30ce\u306e\u516c\u7406\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac"},"content":{"rendered":"

\u30da\u30a2\u30ce\u516c\u7406<\/strong>\u306f\u3001\u6570\u5b66\u306b\u304a\u3044\u3066\u3001\u7b97\u8853\u3092\u5b9a\u7fa9\u3059\u308b\u305f\u3081\u306b\u30b8\u30e5\u30bc\u30c3\u30da \u30da\u30a2\u30ce\u306b\u3088\u3063\u3066\u63d0\u6848\u3055\u308c\u305f\u4e00\u9023\u306e 2 \u6b21\u516c\u7406\u3067\u3059 [ 1 ]\u3002<\/p>

\u516c\u7406<\/span><\/h2>

\u30da\u30a2\u30ce\u306e\u81ea\u7136\u6570\u306e\u516c\u7406\u7684\u5b9a\u7fa9\u306f\u3001\u901a\u5e38\u3001\u6b21\u306e 5 \u3064\u306e\u516c\u7406\u306b\u3088\u3063\u3066\u975e\u516c\u5f0f\u306b\u8a18\u8ff0\u3055\u308c\u307e\u3059\u3002<\/p>

  1. \u30bc\u30ed<\/a><\/span>\u3068\u547c\u3070\u308c\u308b\u8981\u7d20\u306f0<\/span>\u3067\u3042\u308a\u3001\u81ea\u7136\u6570<\/a><\/span>\u3067\u3059\u3002<\/li>
  2. \u3059\u3079\u3066\u306e<\/a><\/span>\u81ea\u7136\u6570n \u306b<\/i><\/span>\u306f\u3001 s<\/i> ( n<\/i> )<\/span>\u307e\u305f\u306f<\/i>Sn<\/i><\/span>\u3067\u793a\u3055\u308c\u308b\u4e00\u610f\u306e\u5f8c\u7d9a\u6570\u304c\u3042\u308a\u307e\u3059\u3002<\/li>
  3. \u5f8c\u7d9a\u306e0 \u3092<\/span>\u6301\u305f\u306a\u3044\u81ea\u7136\u6570\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/li>
  4. \u540c\u3058\u5f8c\u7d9a\u3092\u6301\u3064 2 \u3064\u306e\u81ea\u7136\u6570\u306f\u7b49\u3057\u3044\u3002<\/li>
  5. \u81ea\u7136\u6570\u306e\u30bb\u30c3\u30c8<\/a><\/span>\u306b0 \u304c<\/span>\u542b\u307e\u308c\u3001\u305d\u306e\u5404\u8981\u7d20\u306e\u5f8c\u7d9a\u5024\u304c\u542b\u307e\u308c\u308b\u5834\u5408\u3001\u3053\u306e\u30bb\u30c3\u30c8\u306f\u6b21\u3068\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002
    $$ {\\mathbb{N}} $$<\/div> \u3002<\/li><\/ol>

    \u6700\u521d\u306e\u516c\u7406\u306b\u3088\u308a<\/a><\/span>\u3001\u81ea\u7136\u6574\u6570\u306e\u30bb\u30c3\u30c8\u306f\u7a7a\u3067<\/a><\/span>\u306f\u306a\u3044\u3053\u3068\u304c\u8ff0\u3079\u3089\u308c\u30013 \u756a\u76ee\u306e\u516c\u7406\u3067\u306f\u6700\u521d\u306e\u8981\u7d20\u304c\u3042\u308b\u3053\u3068\u304c\u30015 \u756a\u76ee\u306e\u516c\u7406\u3067\u306f\u6f38\u5316\u6027\u306e\u539f\u7406\u304c\u691c\u8a3c\u3055\u308c\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>

    \u3088\u308a\u6b63\u5f0f\u306b\u306f\u3001\u30c8\u30ea\u30d7\u30ec\u30c3\u30c8

    $$ {\\left(E,x,s\\right)} $$<\/div>\u6b21\u306e\u7279\u6027\u3092\u6e80\u305f\u3057\u307e\u3059\u3002<\/p>
    1. E<\/i><\/span>\u306f\u96c6\u5408\u3001 x<\/i><\/span>\u306fE<\/i><\/span>\u306e\u8981\u7d20\u3001 s \u306f<\/i><\/span>E<\/i><\/span>\u81ea\u4f53\u306e\u30de\u30c3\u30d7\u3067\u3059\u3002 <\/li>
    2. $$ {x \\notin s\\left(E\\right)} $$<\/div><\/li>
    3. s\u306f<\/i><\/span>\u5358\u5c04\u3067\u3059<\/li>
    4. x \u3092<\/i><\/span>\u542b\u307f\u3001 s<\/i><\/span>\u306b\u3088\u3063\u3066\u5b89\u5b9a\u3057\u3066\u3044\u308bE<\/i><\/span>\u306e\u4efb\u610f\u306e\u30b5\u30d6\u30bb\u30c3\u30c8<\/a><\/span>F<\/i><\/span> (\u3064\u307e\u308a\u3001
      $$ {s\\left(F\\right) \\subset F} $$<\/div> ) \u306fE<\/i><\/span>\u306b\u7b49\u3057\u3044\u3002<\/li><\/ol>

      \u3053\u306e\u3088\u3046\u306a\u69cb\u9020\u306f\u3001(\u6570\u5b66\u8005<\/a><\/span>\u30ea\u30c1\u30e3\u30fc\u30c9\u30fb\u30c7\u30c7\u30ad\u30f3\u30c8\u306b\u3061\u306a\u3093\u3067) \u30c7\u30c7\u30ad\u30f3\u30c8\u30fb\u30da\u30a2\u30ce\u69cb\u9020\u3068\u547c\u3070\u308c\u307e\u3059 [ 2 ]<\/p>

      \n\"\u30da\u30a2\u30ce\u306e\u516c\u7406\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\"<\/figure>

      \u30da\u30a2\u30ce\u7b97\u8853<\/a><\/span><\/span><\/h2>

      \u30da\u30a2\u30ce\u7b97\u8853\u306f\u3001\u4e00\u6b21\u7b97\u8853\u306e\u8a00\u8a9e\u306b\u5bfe\u3059\u308b\u30da\u30a2\u30ce\u516c\u7406<\/a><\/span>\u306e\u5236\u9650\u3067\u3059\u3002

      $$ {\\{0,s,+,\\cdot \\}} $$<\/div> \u3002\u8a00\u8a9e\u5909\u6570\u306f\u3001\u89e3\u91c8\u30c9\u30e1\u30a4\u30f3\u5185\u306e\u30aa\u30d6\u30b8\u30a7\u30af\u30c8 (\u3053\u3053\u3067\u306f\u6574\u6570) \u3092\u6307\u5b9a\u3057\u307e\u3059\u3002\u3053\u306e\u4e00\u6b21\u8a00\u8a9e\u3067\u306f\u3001\u6574\u6570\u306e\u30bb\u30c3\u30c8\u306b\u5bfe\u3059\u308b\u5909\u6570\u304c\u306a\u304f\u3001\u3053\u308c\u3089\u306e\u30bb\u30c3\u30c8\u3092\u5b9a\u91cf\u5316\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u524d\u306e\u6bb5\u843d\u306e\u3088\u3046\u306a\u30b9\u30c6\u30fc\u30c8\u30e1\u30f3\u30c8 (\u300c\u4efb\u610f\u306e\u30b5\u30d6\u30bb\u30c3\u30c8…\u300d) \u3067\u7e70\u308a\u8fd4\u3057\u3092\u76f4\u63a5\u8868\u73fe\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002\u6b21\u306b\u3001\u6b21\u306e\u90e8\u5206\u96c6\u5408\u3092\u8003\u616e\u3057\u307e\u3059\u3002
      $$ {\\mathbb N} $$<\/div>\u306f\u305d\u306e\u8981\u7d20\u306e\u30d7\u30ed\u30d1\u30c6\u30a3\u3001\u3064\u307e\u308a\u7b97\u8853\u8a00\u8a9e\u3067\u8a18\u8ff0\u3059\u308b\u30d7\u30ed\u30d1\u30c6\u30a3\u306b\u3088\u3063\u3066\u8868\u73fe\u3055\u308c\u307e\u3059\u3002<\/p>

      \u30da\u30a2\u30ce\u306e\u516c\u7406\u306f\u6b21\u306e 7 \u3064\u306e\u516c\u7406\u306b\u306a\u308a\u3001\u3053\u308c\u306b\u53cd\u5fa9\u306e\u305f\u3081\u306b\u516c\u7406\u306e\u30b9\u30ad\u30fc\u30de<\/i>\u304c\u8ffd\u52a0\u3055\u308c\u307e\u3059\u3002\u3053\u308c\u306f\u516c\u7406\u306e\u53ef\u7b97\u7121\u9650<\/i>(\u8a00\u8a9e\u306e\u5404\u5f0f\u306e\u516c\u7406) \u3092\u8868\u3057\u307e\u3059\u3002 <\/p>

      1. $$ {\\forall x \\lnot (sx = 0)} $$<\/div><\/li>
      2. $$ {\\forall x \\exists y (\\lnot x=0 \\rightarrow sy=x )} $$<\/div><\/li>
      3. $$ {\\forall x \\forall y (sx=sy \\rightarrow x=y)} $$<\/div><\/li>
      4. $$ {\\forall x (x+0=x)} $$<\/div><\/li>
      5. $$ {\\forall x \\forall y (x+sy = s(x+y))} $$<\/div><\/li>
      6. $$ {\\forall x (x\\cdot 0=0)} $$<\/div><\/li>
      7. $$ {\\forall x \\forall y (x\\cdot Sy = (x\\cdot y) + x)} $$<\/div><\/li>
      8. \u3042\u3089\u3086\u308b\u5f0f\u306b\u5bfe\u3057\u3066
        $$ {\\phi(x,x_1,\\ldots,x_n)} $$<\/div> n<\/i> + 1 \u500b\u306e<\/span>\u81ea\u7531\u5909\u6570\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001
        $$ {\\forall x_1 \\ldots \\forall x_n \\left( \\left(\\phi \\left(0,x_1,\\ldots ,x_n \\right) \\wedge \\forall x \\left(\\phi \\left(x,x_1,\\ldots ,x_n \\right)\\rightarrow \\phi \\left(Sx,x_1,\\ldots ,x_n \\right) \\right) \\right)\\rightarrow \\forall x \\phi \\left(x,x_1,\\ldots,x_n \\right) \\right)} $$<\/div><\/li><\/ol>

        \u516c\u7406\u56f3\u306f\u6f38\u5316\u5f0f\u3092\u3046\u307e\u304f\u8868\u73fe\u3057\u3066\u3044\u307e\u3059\u3002

        $$ {\\phi(x,x_1,\\ldots,x_n)} $$<\/div> \u3001\u5909\u6570
        $$ {(x_1,\\ldots,x_n)} $$<\/div>\u306f\u30d1\u30e9\u30e1\u30fc\u30bf\u3067\u3042\u308a\u3001\u4efb\u610f\u306e\u6574\u6570\u306b\u7f6e\u304d\u63db\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059
        $$ {(p_1,\\ldots,p_n)} $$<\/div> \u3002\u5f0f\u306e\u516c\u7406
        $$ {\\phi(x,x_1,\\ldots,x_n)} $$<\/div>\u306b\u306a\u308b\u3001\u9069\u7528\u3055\u308c\u308b
        $$ {(p_1,\\ldots,p_n)} $$<\/div> :<\/p>

        \u305d\u308c\u3092\u660e\u78ba\u306b\u8868\u73fe\u3057\u3066\u3044\u308b\u306e\u306f\u3001\u5168\u4f53\u304c

        $$ {\\left\\{x \\in \\mathbb N\\mid \\phi \\left(x,p_1,\\ldots,p_n \\right)\\right\\}} $$<\/div> 0<\/span>\u304c\u542b\u307e\u308c\u3066\u304a\u308a\u3001\u305d\u306e\u5404\u8981\u7d20\u306e\u5f8c\u7d9a\u8981\u7d20\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u5834\u5408\u306f\u3001
        $$ {\\mathbb N} $$<\/div> \u3002<\/p>

        \u305f\u3060\u3057\u3001\u516c\u7406\u30b9\u30ad\u30fc\u30e0\u306f\u3053\u306e\u30d7\u30ed\u30d1\u30c6\u30a3\u3092\u6b21\u306e\u30b5\u30d6\u30bb\u30c3\u30c8\u306b\u5bfe\u3057\u3066\u306e\u307f\u63d0\u4f9b\u3057\u307e\u3059\u3002

        $$ {\\mathbb N} $$<\/div>\u3053\u308c\u3089\u306f\u4e00\u6b21\u7b97\u8853\u306e\u8a00\u8a9e\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059: \u306e\u90e8\u5206\u96c6\u5408\u306e\u53ef\u7b97\u7121\u9650\u5927
        $$ {\\mathbb N} $$<\/div> \u3002<\/p>

        \u8a00\u8a9e\u3092\u5909\u66f4\u3057\u306a\u3044\u9650\u308a\u3001\u30da\u30a2\u30ce\u306e\u7b97\u8853\u306f\u6709\u9650\u516c\u7406\u5316\u3067\u304d\u306a\u3044\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u516c\u7406\u3092\u6700\u5c0f\u5316\u3057\u3088\u3046\u3068\u3059\u308b\u3053\u3068\u306f\u5fc5\u305a\u3057\u3082\u610f\u5473<\/a><\/span>\u304c\u3042\u308a\u307e\u305b\u3093\u3002\u516c\u7406 2 \u304c\u524a\u9664\u3055\u308c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u3053\u3068\u306b\u307e\u3060\u6c17\u3065\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u30b1\u30fc\u30b9 0 \u3092\u5f8c\u7d9a\u30b1\u30fc\u30b9\u304b\u3089\u533a\u5225\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u305f\u3081\u3001\u304b\u306a\u308a\u7279\u7570\u306a\u518d\u767a\u3067\u3042\u308b\u518d\u767a\u306b\u3088\u3063\u3066\u8a3c\u660e\u3055\u308c\u307e\u3059\u304c\u3001\u5f8c\u8005\u306e\u5834\u5408\u3001\u518d\u767a\u306e\u4eee\u8aac\u306f\u5f79\u306b\u7acb\u3061\u307e\u305b\u3093\u3002<\/p>

        \u5b58\u5728\u611f\u3068\u72ec\u81ea\u6027<\/span><\/h2>

        \u30c7\u30c7\u30ad\u30f3\u30c8\u30fb\u30da\u30a2\u30ce\u69cb\u9020\u306e\u5b58\u5728\u306f\u3001\u96c6\u5408\u8ad6<\/a><\/span>\u306e\u67a0\u7d44\u307f\u306b\u304a\u3051\u308b\u975e\u5e38\u306b\u4e00\u822c\u7684\u306a\u69cb\u9020\u306b\u3088\u3063\u3066\u78ba\u7acb\u3067\u304d\u307e\u3059\u3002<\/p>