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arXiv · 1503.00318

Constructing many atomic models in $\aleph_1$

John T. Baldwin·Michael C. Laskowski·Saharon Shelah
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Abstract

We introduce the notion of pseudo-algebraicity to study atomic models of first order theories (equivalently models of a complete sentence of $L_{\omega_1,\omega}$. Theorem: Let $T$ be any complete first-order theory in a countable language with an atomic model. If the pseudo-minimal types are not dense, then there are $2^{\aleph_1}$ pairwise non-isomorphic atomic models of $T$, each of size $\aleph_1$.

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John T. Baldwin, Michael C. Laskowski, Saharon Shelah. 2015-03-01. Constructing many atomic models in $\aleph_1$. https://arxiv.org/abs/1503.00318

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