On Löwenheim-Skolem-Tarski numbers for extensions of first order logic

Menachem Magidor*, Jouko Väänänen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

We show that, assuming the consistency of a supercompact cardinal, the first (weakly) inaccessible cardinal can satisfy a strong form of a Löwenheim-Skolem-Tarski theorem for the equicardinality logic L(I), a logic introduced in [5] strictly between first order logic and second order logic. On the other hand we show that in the light of present day inner model technology, nothing short of a supercompact cardinal suffices for this result. In particular, we show that the Löwenheim-Skolem-Tarski theorem for the equicardinality logic at κ implies the Singular Cardinals Hypothesis above κ as well as Projective Determinacy.

Original languageEnglish
Pages (from-to)87-113
Number of pages27
JournalJournal of Mathematical Logic
Volume11
Issue number1
DOIs
StatePublished - Jun 2011

Keywords

  • equicardinality quantifier
  • Härtig-quantifier
  • Löwenheim-Skolem theorem
  • supercompact cardinal

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