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

Sgro, J. A.

doi:10.1090/S0002-9939-1980-0556634-4

Interpolation fails for the Souslin-Kleene closure of the open set quantifier logic
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by J. A. Sgro

Proc. Amer. Math. Soc. 78 (1980), 568-572

DOI: https://doi.org/10.1090/S0002-9939-1980-0556634-4

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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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