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Model theory is the branch of mathematical logic which deals with the connection between a formal language and its interpretations, or models.

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Need proof on a model being elementarily equivalent but non-isomorphic

To show that the models are not isomorphic assume an isomorphism $f:\frak{A}\to\frak{B}$, take $(a_n)_{n\in\omega}$ be an increasing sequence such $a_i,a_j$ are from a different copy of $\Bbb Z$ for e …
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10 votes
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The additive structure of clusters of nonstandard models of arithmetic

Given $\frak M$ a countable nonstandard model of $\sf PA$ and let $a\in M$ be a nonstandard element. A "cluster around $a$" is the set of successors and predecessors of $a$, a cluster is a subset of $ …
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