Israel Journal of Mathematics

, Volume 32, Issue 2–3, pp 257–281 | Cite as

New axiomatizations for logics with generalized quantifiers

  • Victor Harnik
  • Michael Makkai


We give a complete axiomatization for admissible fragments ofL {ie257-1}(Q). This axiomatization implies syntactically Gregory’s characterization ofL {ie257-2} sentences with no uncountable models ([5]). This is then extended to stationary logic. To obtain these results, we employ Ressayre’s methods ([16], [17]) augmented with an application of game sentences. In section 4 we prove a result emphasizing the naturalness of Gregory’s result.


Deductive System Generalize Quantifier Completeness Theorem Weak Model Good Extension 
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Copyright information

© The Weizmann Science Press of Israel 1979

Authors and Affiliations

  • Victor Harnik
    • 1
    • 2
  • Michael Makkai
    • 1
    • 2
  1. 1.University of HaifaHaifaIsrael
  2. 2.McGill UniversityMontreal P.Q.Canada

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