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The logical consequence relation of propositional tense logic
Author(s) -
Thomason S. K.
Publication year - 1975
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19750210104
Subject(s) - mathematics , well formed formula , kripke semantics , modal logic , propositional calculus , intermediate logic , cardinality (data modeling) , propositional variable , recursion (computer science) , zeroth order logic , intuitionistic logic , autoepistemic logic , semantics (computer science) , discrete mathematics , classical logic , modal , multimodal logic , computer science , algorithm , artificial intelligence , description logic , programming language , chemistry , polymer chemistry , data mining
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 γ m such that all models of γ m are isomorphic and have cardinality x m , where x 0 = χ 0 , x m+1 = 2 xm , and x ω = lim{ x m < | 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.