Complete Lω1,ω‐sentences with maximal models in multiple cardinalities

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Mathematical Logic Quarterly 65 (4):444-452 (2019)
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Abstract

In [5], examples of incomplete sentences are given with maximal models in more than one cardinality. The question was raised whether one can find similar examples of complete sentences. In this paper, we give examples of complete ‐sentences with maximal models in more than one cardinality. From (homogeneous) characterizability of κ we construct sentences with maximal models in κ and in one of and more. Indeed, consistently we find sentences with maximal models in uncountably many distinct cardinalities.

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10.1002/malq.201800010

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Citations of this work

Hanf numbers for extendibility and related phenomena.John T. Baldwin & Saharon Shelah - 2022 - Archive for Mathematical Logic 61 (3):437-464.

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References found in this work

A complete L ω1ω-sentence characterizing ℵ1.Julia F. Knight - 1977 - Journal of Symbolic Logic 42 (1):59-62.
On the existence of atomic models.M. C. Laskowski & S. Shelah - 1993 - Journal of Symbolic Logic 58 (4):1189-1194.

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