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A strong failure of $$\aleph _0$$ ℵ 0 -stability for atomic classes
Archive for Mathematical Logic 58 (1-2):99-118 (2019)
Abstract
We study classes of atomic models \ of a countable, complete first-order theory T. We prove that if \ is not \-small, i.e., there is an atomic model N that realizes uncountably many types over \\) for some finite \ from N, then there are \ non-isomorphic atomic models of T, each of size \.Links
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References found in this work
Logic with the quantifier “there exist uncountably many”.H. Jerome Keisler - 1970 - Annals of Mathematical Logic 1 (1):1-93.
Logic with the quantifier "there exist uncountably many".H. Jerome Keisler - 1970 - Annals of Mathematical Logic 1 (1):1.
Classification Theory and the Number of Nonisomorphic Models.S. Shelah - 1982 - Journal of Symbolic Logic 47 (3):694-696.
Iterated elementary embeddings and the model theory of infinitary logic.John T. Baldwin & Paul B. Larson - 2016 - Annals of Pure and Applied Logic 167 (3):309-334.
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