Vaught’s Conjecture Without Equality

Notre Dame Journal of Formal Logic 56 (4):573-582 (2015)
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Abstract

Suppose that $\sigma\in{\mathcal{L}}_{\omega _{1},\omega }$ is such that all equations occurring in $\sigma$ are positive, have the same set of variables on each side of the equality symbol, and have at least one function symbol on each side of the equality symbol. We show that $\sigma$ satisfies Vaught’s conjecture. In particular, this proves Vaught’s conjecture for sentences of $ {\mathcal{L}}_{\omega _{1},\omega }$ without equality.

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References found in this work

The number of countable models.Michael Morley - 1970 - Journal of Symbolic Logic 35 (1):14-18.
Vaught's conjecture for o-minimal theories.Laura L. Mayer - 1988 - Journal of Symbolic Logic 53 (1):146-159.

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