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On the existence of atomic models

Published online by Cambridge University Press:  12 March 2014

M. C. Laskowski
Department of Mathematics, University of Maryland, College Park, Maryland 20742, E-mail:
S. Shelah
Department of Mathematics, The Hebrew University, Jerusalem, Israel Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903


We give an example of a countable theory T such that for every cardinal λ ≥ ℵ2 there is a fully indiscernible set A of power λ 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 λ where the principal types are dense, yet T(A) has no atomic model.

Research Article
Copyright © Association for Symbolic Logic 1993

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