A completeness theorem in modal logic
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The present paper attempts to state and prove a completeness theorem for the system S5 of [1], supplemented by first-order quantifiers and the sign of equality. We assume that we possess a denumerably infinite list of individual variables a, b, c, …, x, y, z, …, xm, ym, zm, … as well as a denumerably infinite list of n-adic predicate variables Pn, Qn, Rn, …, Pmn, Qmn, Rmn,…; if n=0, an n-adic predicate variable is often called a “propositional variable.” A formula Pn(x1, …,xn) is an n-adic prime formula; often the superscript will be omitted if such an omission does not sacrifice clarity.
2019 ◽
Vol 12
(2)
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pp. 255-270
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2015 ◽
Vol 8
(3)
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pp. 467-487
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2019 ◽
Vol 29
(8)
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pp. 1311-1344
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2011 ◽
Vol 278
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pp. 129-143
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