AbstractThis work concerns the model theory of propositional tense logic with the Kripke relational semantics. It is shown (i) that there is a formulaywhose logical consequences form a complete II set, and (ii) that for 0 ≦m<ω+ω there are formulas γmsuch that all models of γmare isomorphic and have cardinalityxm, wherex0= χ0,xm+1=2xm, andxω= lim{xm<|mω}. 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