Plaza Representation of Strict Closure Space
نویسنده
چکیده
We define strict closure space algebras as Boolean algebras augmented with a unary operation Int that satisfies conditions analogous to those of the interior operation from strict closure spaces. We also consider a first order modal logic SCS in which the necessity operator satisfies analogous conditions. Sikorski proved that every interior algebra can be represented as an algebra of subsets of a zero-dimensional topological space X ⊆ [2]; in this paper we prove an analogous result for strict closure space algebras. We also prove representability of Tarski-Lindenbaum algebras of SCS-theories in first-order languages of arbitrary cardinality.
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