The Hanf number in the strictly stable case

Mathematical Logic Quarterly 66 (3):280-294 (2020)
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Abstract

We associate Hanf numbers to triples where T and T1 are theories and p is a type. We show that the Hanf number for the property: “there is a model M1 of which omits p, but is saturated” is larger than the Hanf number of but smaller than the Hanf number of when T is stable with. In fact, surprisingly, we even characterise the Hanf number of when we fix where T is a first order complete (and stable), and demand.

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10.1002/malq.201900021

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Classification Theory and the Number of Nonisomorphic Models.S. Shelah - 1982 - Journal of Symbolic Logic 47 (3):694-696.

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