Title: Separating Models by Formulas and the Number of Countable Models
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 ...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 $CH$).Read More
Publication Year: 2012
Publication Date: 2012-11-23
Language: en
Type: preprint
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Cited By Count: 3
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