Israel Journal of Mathematics

, Volume 19, Issue 4, pp 359–368 | Cite as

Finiteness in not a ∑0-Property

  • H. Gaifman


We construct a sequence of transitive finite setsA n ,n∈ω, such that, puttingA = U n∈ω A n ,A is transitive of rank ω (without urelements) and, for every sentence Φ in the language of set theory,Aφ if and only ifA n φ, for all but finitely manyn’s. This implies the claim of the title.


Binary Relation Free Variable Function Symbol Main Claim Sentential Connective 
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Copyright information

© Hebrew University 1975

Authors and Affiliations

  • H. Gaifman
    • 1
  1. 1.Department of MathematicsThe Hebrew University of JerusalemJerusalemIsrael

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