Knight's model, its automorphism group, and characterizing the uncountable cardinals

Journal of Mathematical Logic 2 (01):113-144 (2002)
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Abstract

We show that every ℵα can be characterized by the Scott sentence of some countable model; moreover there is a countable structure whose Scott sentence characterizes ℵ1 but whose automorphism group fails the topological Vaught conjecture on analytic sets. We obtain some partial information on Ulm type dichotomy theorems for the automorphism group of Knight's model.

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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.
Infinitary logic.John L. Bell - 2008 - Stanford Encyclopedia of Philosophy.

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References found in this work

An example concerning Scott heights.M. Makkai - 1981 - Journal of Symbolic Logic 46 (2):301-318.
A complete L ω1ω-sentence characterizing ℵ1.Julia F. Knight - 1977 - Journal of Symbolic Logic 42 (1):59-62.
On automorphism groups of countable structures.Su Gao - 1998 - Journal of Symbolic Logic 63 (3):891-896.

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