ag-gipp/GoUldI

{
  "definitions" : {
    "Con" : [ {
      "Q1319773" : "Consistency"
    } ],
    "ZF" : [ {
      "Q45412642" : "Zermelo–Fraenkel set theory without choice"
    } ],
    "AC" : [ {
      "Q179692" : "Axiom of choice"
    } ],
    "\\neg" : [ {
      "Q190558" : "Negation"
    } ]
  },
  "constraints" : [ ],
  "math_inputtex" : "Con(ZF+\\neg AC)",
  "math_inputtex_semantic" : "\\wf{Q1319773}{\\operatorname{Con}}(\\w{Q45412642}{\\operatorname{ZF}} + \\w{Q190558}{\\neg} \\w{Q179692}{\\operatorname{AC}})",
  "correct_tex" : "Con(ZF+\\neg AC)",
  "correct_mml" : "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"p1.1.m1.1\" class=\"ltx_Math\" alttext=\"\\operatorname{Con}(\\operatorname{ZF}+\\neg\\operatorname{AC})\" display=\"inline\">\n  <semantics id=\"p1.1.m1.1a\">\n    <mrow id=\"p1.1.m1.1.12.2\" xref=\"p1.1.m1.1.12.1.cmml\">\n      <mi id=\"p1.1.m1.1.3\" xref=\"p1.1.m1.1.3.cmml\">Con</mi>\n      <mo id=\"p1.1.m1.1.12.2a\" xref=\"p1.1.m1.1.12.1.cmml\">⁡</mo>\n      <mrow id=\"p1.1.m1.1.12.2.2\" xref=\"p1.1.m1.1.12.1.cmml\">\n        <mo stretchy=\"false\" id=\"p1.1.m1.1.4\" xref=\"p1.1.m1.1.12.1.cmml\">(</mo>\n        <mrow id=\"p1.1.m1.1.12.2.1\" xref=\"p1.1.m1.1.12.2.1.cmml\">\n          <mi id=\"p1.1.m1.1.6\" xref=\"p1.1.m1.1.6.cmml\">ZF</mi>\n          <mo id=\"p1.1.m1.1.7\" xref=\"p1.1.m1.1.7.cmml\">+</mo>\n          <mrow id=\"p1.1.m1.1.12.2.1.1\" xref=\"p1.1.m1.1.12.2.1.1.cmml\">\n            <mi mathvariant=\"normal\" id=\"p1.1.m1.1.8\" xref=\"p1.1.m1.1.8.cmml\">¬</mi>\n            <mo id=\"p1.1.m1.1.12.2.1.1.1\" xref=\"p1.1.m1.1.12.2.1.1.1.cmml\">⁢</mo>\n            <mi id=\"p1.1.m1.1.10\" xref=\"p1.1.m1.1.10.cmml\">AC</mi>\n          </mrow>\n        </mrow>\n        <mo stretchy=\"false\" id=\"p1.1.m1.1.11\" xref=\"p1.1.m1.1.12.1.cmml\">)</mo>\n      </mrow>\n    </mrow>\n    <annotation-xml encoding=\"MathML-Content\" id=\"p1.1.m1.1b\">\n      <apply id=\"p1.1.m1.1.12.1.cmml\" xref=\"p1.1.m1.1.12.2\">\n        <csymbol cd=\"latexml\" id=\"p1.1.m1.1.3.cmml\" xref=\"p1.1.m1.1.3\">Q1319773</csymbol>\n        <apply id=\"p1.1.m1.1.12.2.1.cmml\" xref=\"p1.1.m1.1.12.2.1\">\n          <plus id=\"p1.1.m1.1.7.cmml\" xref=\"p1.1.m1.1.7\"/>\n          <csymbol cd=\"latexml\" id=\"p1.1.m1.1.6.cmml\" xref=\"p1.1.m1.1.6\">Q45412642</csymbol>\n          <apply id=\"p1.1.m1.1.12.2.1.1.cmml\" xref=\"p1.1.m1.1.12.2.1.1\">\n            <times id=\"p1.1.m1.1.12.2.1.1.1.cmml\" xref=\"p1.1.m1.1.12.2.1.1.1\"/>\n            <csymbol cd=\"latexml\" id=\"p1.1.m1.1.8.cmml\" xref=\"p1.1.m1.1.8\">Q190558</csymbol>\n            <csymbol cd=\"latexml\" id=\"p1.1.m1.1.10.cmml\" xref=\"p1.1.m1.1.10\">Q179692</csymbol>\n          </apply>\n        </apply>\n      </apply>\n    </annotation-xml>\n    <annotation encoding=\"application/x-tex\" id=\"p1.1.m1.1c\">\\operatorname{Con}(\\operatorname{ZF}+\\neg\\operatorname{AC})</annotation>\n  </semantics>\n</math>",
  "uri" : "https://arxiv.org/abs/math/9209209",
  "title" : "Consistency proofs of ZFC extensions",
  "comment" : "create ZF as a facet of ZFC?",
  "type" : "general formula",
  "ntcir12-type" : "27",
  "formula" : "1_64.5",
  "page" : "10",
  "ntcir12-relevance" : "4"
}