Separating Models by Formulas and the Number of Countable Models

Mohammad Assem

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arXiv · 1211.5441

Separating Models by Formulas and the Number of Countable Models

Mohammad Assem

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Abstract

We indicate a way of distinguishing between structures, for which, two structures are said to be separable.Being separable implies being non-isomorphic. We show that for any first order theory $T$ in a countable language, if it has an uncountable set of countable models that are pairwise separable, then actually it has such a set of size $2^{\aleph_0}$. Our result follows trivially assuming the Continuum Hypothesis ($CH$). We work here in $ZFC$ (only without $CH$).

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BibTeX RIS

Mohammad Assem. 2012-11-27. Separating Models by Formulas and the Number of Countable Models. https://arxiv.org/abs/1211.5441

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