On the number of -equivalent non-isomorphic models

Authors:
Saharon Shelah and Pauli Väisänen

Journal:
Trans. Amer. Math. Soc. **353** (2001), 1781-1817

MSC (2000):
Primary 03C55; Secondary 03C75, 03E05

DOI:
https://doi.org/10.1090/S0002-9947-00-02604-0

Published electronically:
December 29, 2000

MathSciNet review:
1707477

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

We prove that if is consistent then is consistent with the following statement: There is for every a model of cardinality which is -equivalent to exactly non-isomorphic models of cardinality . 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 and positive integer it is consistent with that there is a ``good'' ladder system having exactly pairwise nonequivalent colourings.

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Additional Information

**Saharon Shelah**

Affiliation:
Institute of Mathematics, The Hebrew University, Jerusalem, Israel and Rutgers University, Hill Ctr-Busch, New Brunswick, New Jersey 08903

Email:
shelah@math.huji.ac.il

**Pauli Väisänen**

Affiliation:
Department of Mathematics, P.O. Box 4, 00014 University of Helsinki, Finland

Email:
pauli.vaisanen@helsinki.fi

DOI:
https://doi.org/10.1090/S0002-9947-00-02604-0

Keywords:
Number of models,
ladder system,
uniformization,
infinitary logic,
iterated forcing

Received by editor(s):
April 28, 1997

Published electronically:
December 29, 2000

Additional Notes:
The first author thanks GIF for its support of this research, and also the University of Helsinki for funding a visit of the first author to Helsinki in August 1996. This is his paper number 646.

This paper is the second author’s Licentiate’s thesis. The second author did his share of the paper under the supervision of Tapani Hyttinen.

Article copyright:
© Copyright 2000
American Mathematical Society