Löb's theorem

proper noun

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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Meanings

proper noun
  1. human sciencesA 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.

Origin

Named after Martin Löb, who formulated it in 1955.

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Cite this entry
APA

Löb's theorem. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/L%C3%B6b's%20theorem

MLA

“Löb's theorem.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/L%C3%B6b's%20theorem. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “Löb's theorem,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/L%C3%B6b's%20theorem.

Source: Löb's theorem on Wiktionary, CC BY-SA 4.0.