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Interpolation Fails for the Souslin-Kleene Closure of the Open Set Quantifier Logic

J. A. Sgro
Proceedings of the American Mathematical Society
Vol. 78, No. 4 (Apr., 1980), pp. 568-572
DOI: 10.2307/2042433
Stable URL: http://www.jstor.org/stable/2042433
Page Count: 5
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Interpolation Fails for the Souslin-Kleene Closure of the Open Set Quantifier Logic
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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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