On the strong Martin conjecture

Journal of Symbolic Logic 56 (3):862-875 (1991)
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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 L1(T), or ii) some complete extension of T in L1 has continuum many L1-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 L2-types

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References found in this work

Model Theory.Michael Makkai, C. C. Chang & H. J. Keisler - 1991 - Journal of Symbolic Logic 56 (3):1096.
Classification Theory and the Number of Nonisomorphic Models.S. Shelah - 1982 - Journal of Symbolic Logic 47 (3):694-696.
An Introduction to Stability Theory.Anand Pillay - 1986 - Journal of Symbolic Logic 51 (2):465-467.
On Martin's conjecture.C. M. Wagner - 1982 - Annals of Mathematical Logic 22 (1):47.

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