Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On models $\equiv _{\infty \omega }$ to an uncountable model
HTML articles powered by AMS MathViewer

by Mark Nadel PDF
Proc. Amer. Math. Soc. 54 (1976), 307-310 Request permission

Abstract:

It is shown that a model is ${ \equiv _{\infty \omega }}$ to an uncountable model provided there is an uncountable model of its complete theory with respect to some admissible fragment containing a copy of the given model.
References
  • Jon Barwise, Admissible sets and structures, Perspectives in Mathematical Logic, Springer-Verlag, Berlin-New York, 1975. An approach to definability theory. MR 0424560, DOI 10.1007/978-3-662-11035-5
  • John Gregory, Uncountable models and infinitary elementary extensions, J. Symbolic Logic 38 (1973), 460–470. MR 376338, DOI 10.2307/2273044
  • V. Harnik, Topics in ${L_{{\omega _1}\omega }}$, Dartmouth, Winter term 1974 (mimeographed). M. Makkai, Applications of a result on weak definability theory in ${L_{{\omega _1}\omega }}$ (to appear). M. Nadel, Model theory in admissible sets, Doctoral Dissertation, University of Wisconsin, 1971.
  • Mark Nadel, More Lowenheim-Skolem results for admissible sets, Israel J. Math. 18 (1974), 53–64. MR 366654, DOI 10.1007/BF02758130
  • Mark Nadel, Scott sentences and admissible sets, Ann. Math. Logic 7 (1974), 267–294. MR 384471, DOI 10.1016/0003-4843(74)90017-5
  • J.-P. Ressayre, Models with compactness properties relative to an admissible set (to appear).
Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 54 (1976), 307-310
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0392556-9
  • MathSciNet review: 0392556