"Löb's theorem" meaning in English

{
  "etymology_text": "Named after Martin Löb, who formulated it in 1955.",
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  "lang_code": "en",
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      "glosses": [
        "A theorem stating that, in any formal system F with Peano arithmetic, for any formula P, if it is provable in F that \"if P is provable in F then P is true\", then P is provable in F."
      ],
      "id": "en-Löb's_theorem-en-name-LeiYmq4t",
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        [
          "logic",
          "logic"
        ],
        [
          "formal system",
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        [
          "Peano arithmetic",
          "Peano arithmetic"
        ],
        [
          "formula",
          "formula"
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      "raw_glosses": [
        "(logic) A theorem stating that, in any formal system F with Peano arithmetic, for any formula P, if it is provable in F that \"if P is provable in F then P is true\", then P is provable in F."
      ],
      "topics": [
        "human-sciences",
        "logic",
        "mathematics",
        "philosophy",
        "sciences"
      ],
      "wikipedia": [
        "Löb's theorem",
        "Martin Löb"
      ]
    }
  ],
  "word": "Löb's theorem"
}

{
  "etymology_text": "Named after Martin Löb, who formulated it in 1955.",
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      "args": {},
      "expansion": "Löb's theorem",
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  "lang_code": "en",
  "pos": "name",
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        "en:Logic"
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      "glosses": [
        "A theorem stating that, in any formal system F with Peano arithmetic, for any formula P, if it is provable in F that \"if P is provable in F then P is true\", then P is provable in F."
      ],
      "links": [
        [
          "logic",
          "logic"
        ],
        [
          "formal system",
          "formal system"
        ],
        [
          "Peano arithmetic",
          "Peano arithmetic"
        ],
        [
          "formula",
          "formula"
        ]
      ],
      "raw_glosses": [
        "(logic) A theorem stating that, in any formal system F with Peano arithmetic, for any formula P, if it is provable in F that \"if P is provable in F then P is true\", then P is provable in F."
      ],
      "topics": [
        "human-sciences",
        "logic",
        "mathematics",
        "philosophy",
        "sciences"
      ],
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        "Löb's theorem",
        "Martin Löb"
      ]
    }
  ],
  "word": "Löb's theorem"
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