Hostname: page-component-76fb5796d-zzh7m Total loading time: 0 Render date: 2024-04-25T16:05:28.277Z Has data issue: false hasContentIssue false
  • English
  • Français

Finite inseparability of some theories of cylindrification algebras

Published online by Cambridge University Press:  12 March 2014

Stephen D. Comer
Stephen D. Comer*
Affiliation:
University of Colorado and Vanderbilt University
Get access Rights & Permissions [Opens in a new window]

Extract

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

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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