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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
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2042433
Page Count: 5
You can always find the topics here!Topics: Topological theorems, Interpolation, Topology, Logical theorems, Mathematical theorems, Mathematics, Counterexamples, General topology, Abstract logic, Topological logic
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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.
Proceedings of the American Mathematical Society © 1980 American Mathematical Society