Journal of Symbolic Logic

On the Existence of Atomic Models

M. C. Laskowski and S. Shelah

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We give an example of a countable theory $T$ such that for every cardinal $\lambda \geq \aleph_2$ there is a fully indiscernible set $A$ of power $\lambda$ such that the principal types are dense over $A$, yet there is no atomic model of $T$ over $A$. In particular, $T(A)$ is a theory of size $\lambda$ where the principal types are dense, yet $T(A)$ has no atomic model.

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J. Symbolic Logic, Volume 58, Issue 4 (1993), 1189-1194.

First available in Project Euclid: 6 July 2007

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Laskowski, M. C.; Shelah, S. On the Existence of Atomic Models. J. Symbolic Logic 58 (1993), no. 4, 1189--1194.

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