The logical consequence relation of propositional tense logic

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 x₀ = χ₀, 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.