The complexity of plane hyperbolic incidence geometry is ∀∃∀∃

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


We show that plane hyperbolic geometry, expressed in terms of points and the ternary relation of collinearity alone, cannot be expressed by means of axioms of complexity at most ∀∃∀, but that there is an axiom system, all of whose axioms are ∀∃∀∃ sentences. This remains true for Klingenberg's generalized hyperbolic planes, with arbitrary ordered fields as coordinate fields.

Original languageEnglish (US)
Pages (from-to)277-281
Number of pages5
JournalMathematical Logic Quarterly
Issue number3
StatePublished - Jan 1 2005


  • Hyperbolic geometry
  • Incidence geometry
  • Quantifier complexity

ASJC Scopus subject areas

  • Logic


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