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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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.

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Interpolation fails for the Souslin-Kleene closure of the open set quantifier logic
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by J. A. Sgro PDF
Proc. Amer. Math. Soc. 78 (1980), 568-572 Request permission

Abstract:

In this paper we show that the Souslin-Kleene closure of the open set quantifier logic fails to have interpolation. We also show that the notion of a ${T_0}$-topological space is not definable in this logic. This gives a more natural proof that it is strictly weaker than the interior operator logic.
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 78 (1980), 568-572
  • MSC: Primary 03C80; Secondary 54A99
  • DOI: https://doi.org/10.1090/S0002-9939-1980-0556634-4
  • MathSciNet review: 556634