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On the strong Martin conjecture

Published online by Cambridge University Press:  12 March 2014

Masanori Itai
Masanori Itai*
Affiliation:
Department of Mathematics, St. Lawrence University, Canton, New York 13617
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Abstract

We study the following conjecture.

Conjecture. Let T be an ω-stable theory with continuum many countable models. Then either i) T has continuum many complete extensions in L 1(T), or ii) some complete extension of T in L 1 has continuum many L 1-types without parameters.

By Shelah's proof of Vaught's conjecture for ω-stable theories, we know that there are seven types of ω-stable theory with continuum many countable models. We show that the conjecture is true for all but one of these seven cases. In the last case we show the existence of continuum many L 2-types.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 56 , Issue 3 , September 1991 , pp. 862 - 875
Copyright
Copyright © Association for Symbolic Logic 1991

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