Investigations into the sentential calculus with identity
Bloom (Stephen) & Suszko (Roman)
Source: Notre Dame J. Formal Logic 13, no. 3 (1972), 289–308
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    The sentential calculus with identity (SCI) is obtained from the classical sentential calculus by the addition of a binary 'identity connective' = and axioms which 'say' that p = q means p is identical to q. The study of the semantics of the resulting consequence operation using Tarski's matrix method yields insights into consequence operations in general and the classical and modal1 consequence operations in particular. One finitely axiomatizable SCI theory is studied. It is shown that this theory consists of those formulas valid in all topological Boolean algebras.

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