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 language | English |
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Pages (from-to) | 1781-1817 |
Number of pages | 37 |
Journal | Transactions of the American Mathematical Society |
Volume | 353 |
Issue number | 5 |
DOIs | |
State | Published - 2001 |
Keywords
- Infinitary logic
- Iterated forcing
- Ladder system
- Number of models
- Uniformization