Word.ws English Dictionary

Löb's theorem

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.

Proper noun

Löb's theorem

  1. 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.

Origin of Löb's theorem

Named after Martin Löb, who formulated it in 1955.

Questions about Löb's theorem

What does Löb's theorem mean?
Löb's theorem means 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.
What part of speech is Löb's theorem?
Löb's theorem is a proper noun.

Words near Löb's theorem in the dictionary

  1. Líl̓wat
  2. lóng
  3. lóngs
  4. López
  5. Löb's paradox
  6. Löb's theorem
  7. Löbau
  8. Löffler
  9. Löffler's syndrome
  10. Löfflers
  11. Löfgren syndrome

Source and license

Adapted from Wiktionary: Löb's theorem (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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