Definability with Bounded Number of Bound Variables
نویسندگان
چکیده
A theory satis es the k variable property if every rst order formula is equivalent to a formula with at most k bound variables possibly reused Gabbay has shown that a model of temporal logic satis es the k variable property for some k if and only if there exists a nite 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 rst nite basis theorems for branching time models of temporal logic
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