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A Note on the Realization of Types

Published online by Cambridge University Press:  20 November 2018

Alan Adamson
Alan Adamson*
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo Ont. N2L 3G1 and Mathematical Institute, University of Oxford
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Let L be a countable first-order language and T a fixed complete theory in L. If is a model of T, is an n-sequence of variables, and ā=〈a1,…, an〉 is an n-sequence of elements of M, the universe of , we let where ranges over formulas of L containing freely at most the variables υ1,…υn. ā is said to realize in We let be where is the sequence of the first n variables of L.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 1 , 01 March 1980 , pp. 95 - 98
Copyright
Copyright © Canadian Mathematical Society 1980

References

1. Morley, M., Applications of Topology to Lω1ω, Proceedings of Symposia in Pure Mathematics XXV, A.S.L. Providence, 1974.Google Scholar
2. Robinson, A., Introduction to Model Theory and the Metamathematics of Algebra, North- Holland, Amsterdam 1963.Google Scholar
3. Keisler, H. J., Forcing and the Omitting Types Theorem, Studies in Model Theory, Englewood Cliffs, N.J., 1973.Google Scholar