The logical consequence relation of propositional tense logic |
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Authors: | S. K. Thomason |
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Abstract: | This work concerns the model theory of propositional tense logic with the Kripke relational semantics. It is shown (i) that there is a formula y whose logical consequences form a complete II set, and (ii) that for 0 ≦ m < ω+ ω there are formulas γm such that all models of γm are isomorphic and have cardinality xm, where x0 = χ0, xm+1 = 2xm, and xω = lim{xm < | m ω}. Familiarity with the relational semantics for modal and tense logic ([1] or [3], for example) will be presumed. A knowledge of recursion theory would be helpful, although some background material will be provided. |
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