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Proceedings of the American Mathematical Society

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Interpolation fails for the Souslin-Kleene closure of the open set quantifier logic


Author: J. A. Sgro
Journal: Proc. Amer. Math. Soc. 78 (1980), 568-572
MSC: Primary 03C80; Secondary 54A99
MathSciNet review: 556634
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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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DOI: https://doi.org/10.1090/S0002-9939-1980-0556634-4
Article copyright: © Copyright 1980 American Mathematical Society