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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Effectiveness and Vaught's gap $ \omega $ two-cardinal theorem


Author: James H. Schmerl
Journal: Proc. Amer. Math. Soc. 58 (1976), 237-240
MSC: Primary 02H05; Secondary 02F35
DOI: https://doi.org/10.1090/S0002-9939-1976-0432445-4
MathSciNet review: 0432445
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Abstract: We consider functions $ f$ with the property that whenever $ \sigma $ is a sentence in $ {L_{\omega \omega }}$, then $ f(\sigma ) < \omega $, and if $ \sigma $ has a gap $ > f(\sigma )$ model, then $ \sigma $ admits all types. A question of Barwise is answered by showing that no such $ f$ is recursive, and that the least such $ f$ is not co-r.e.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0432445-4
Keywords: Two-cardinal theorems, transfer theorems
Article copyright: © Copyright 1976 American Mathematical Society