On the number of l1i-equivalent non-isomorphic models

Saharon Shelah*, Pauli Väisänen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We prove that if ZF is consistent then ZFC + GCH is consistent with the following statement: There is for every k < u a model of cardinality N1 which is L1-equivalent to exactly k non-isomorphic models of cardinality N1. In order to get this result we introduce ladder systems and colourings different from the "standard" counterparts, and prove the following purely combinatorial result: For each prime number p and positive integer m it is consistent with ZFC + GHC that there is a "good" ladder system having exactly pm pairwise nonequivalent colourings.

Original languageEnglish
Pages (from-to)1781-1817
Number of pages37
JournalTransactions of the American Mathematical Society
Volume353
Issue number5
DOIs
StatePublished - 2001

Keywords

  • Infinitary logic
  • Iterated forcing
  • Ladder system
  • Number of models
  • Uniformization

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