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Finite inseparability of some theories of cylindrificationalgebras

Published online by Cambridge University Press:  12 March 2014

Stephen D. Comer
Stephen D. Comer*
Affiliation:
University of Colorado and Vanderbilt University
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Extract

An elementary theory T in a language L is (strongly) finitely inseparable if the set of logicallyvalid sentences of L and the set ofT-finitely refutable sentences are recursively inseparable.In §1 we establish a sufficient condition for the elementary theory of aclass of BA's with operators to be finitely inseparable. This is done usingthe methods developed independently by M. Rabin and D. Scott (see [6]) onthe one hand and by Ershov on the other (see [2]).

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 34 , Issue 2 , 25 July 1969 , pp. 171 - 176
Copyright
Copyright © Association for Symbolic Logic 1969

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Footnotes

1

Research supported by a predoctoral NSF Traineeship.

References

[1] Ershov, Yu. L., Decidability of the elementary theory of relatively complemented distributive lattices and the theory of filters, Algebra i logika seminar, vol. 3 (1964), pp. 17–38.Google Scholar
[2] Ershov, Yu. L., Lavrov, I. A., Taimonov, A. D. and Taitslin, M. A., Elementary theories, Russian mathematical surveys, vol. 20 (1965), pp. 35–105.Google Scholar
[3] Feferman, S. and Vaught, R. L., The first order properties of products of algebraic systems, Fundamenta mathematicae, vol. 47 (1959), pp. 57–103.Google Scholar
[4] Henkin, L. and Tarski, A., “Cylindric algebras”, Lattice theory, Proceedings of symposia in pure mathematics, vol. 2, Amer. Math. Soc., Providence, R.I., 1961, pp. 83–113.Google Scholar
[5] Jonsson, B. and Tarski, A., Boolean algebras with operators. I, II, American journal of mathematics, vol. 73 (1951), pp. 891–939; vol. 74 (1952), pp. 127-162.Google Scholar
[6] Rabin, M. O., A simple method for undecidability proofs and some applications, Logic, methodology and the philosophy of science, Proceedings of the 1964 International Congress, North-Holland, Amsterdam, 1965, pp. 58–68.Google Scholar
[7] Tarski, A., Arithmetical classes and types of Boolean algebras, Bulletin of the American Mathematical Society, vol. 55 (1949), p. 64.Google Scholar
[8] Tarski, A., Mostowski, A. and Robinson, R. M., Undecidable theories, North-Holland, Amsterdam, 1953.Google Scholar