Paris-Harrington theorem

proper noun

A theorem stating that a certain combinatorial principle in Ramsey theory, namely the strengthened finite Ramsey theorem, is true, but not provable in Peano arithmetic.

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Meanings

proper nounthe Paris-Harrington theorem
  1. mathematical logicA theorem stating that a certain combinatorial principle in Ramsey theory, namely the strengthened finite Ramsey theorem, is true, but not provable in Peano arithmetic.

Origin

Named after Jeff Paris and Leo Harrington, who carried out work on this topic.

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Cite this entry
APA

Paris-Harrington theorem. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/Paris-Harrington%20theorem

MLA

“Paris-Harrington theorem.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Paris-Harrington%20theorem. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “Paris-Harrington theorem,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/Paris-Harrington%20theorem.

Source: Paris-Harrington theorem on Wiktionary, CC BY-SA 4.0.