Last Updated
：2025/12/02
Löb's theorem
Proper noun
Japanese Meaning
論理学における定理であり、ペアノ算術を含む任意の形式的体系 F において、ある命題 P について「もし P が F 内で証明可能ならば P は真である」と F 側で証明できたならば、P は F 内で証明可能であるということを示す定理。
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(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.
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Löb's theorem
Löb's theorem shows that if a formal system proves that 'if P is provable in the system then P is true', then the system proves P.
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Löb's theorem shows that if a formal system proves that 'if P is provable in the system then P is true', then the system proves P.
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