arXiv math/99081601999-08-30math.LO

On the number of L_{infty,omega_1}-equivalent non-isomorphic models

Saharon Shelah, Pauli Vaisanen

发表信息：: Trans. Amer. Math. Soc. 353 No. 5 (2001) 1781--1817

英文摘要：

We prove that if ZF is consistent then ZFC+GCH is consistent with the following statement: There is for every k<omega a model of cardinality aleph_1 which is L_{infty,omega_1}-equivalent to exactly k non-isomorphic models of cardinality aleph_1. 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+GCH that there is a ``good'' ladder system having exactly p^m pairwise nonequivalent colourings.

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