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- W255293104 abstract "Abstract A theory satisfies the k-variable property if every first-order formula is equivalent to a formula with at most k bound variables (possibly reused). Gabbay has shown that a model of temporal logic satisfies the k -variable property for some k if and only if there exists a finite basis for the temporal connectives over that model. We give a model-theoretic method for establishing the k -variable property, involving a restricted Ehrenfeucht-Fraisse game in which each player has only k pebbles. We use the method to unify and simplify results in the literature for linear orders. We also establish new k -variable properties for various theories of bounded-degree trees, and in each case obtain tight upper and lower bounds on k . This gives the first finite basis theorems for branching-time models of temporal logic." @default.
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- W255293104 date "1987-01-01" @default.
- W255293104 modified "2023-09-24" @default.
- W255293104 title "Definability with Bounded Number of Bound Variables" @default.
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