The Computational Complexity of Logical Theories (Lecture Notes in Mathematics 718) (1979)

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and background.- Ehrenfeucht games and decision procedures.- Integer addition - An example of an Ehrenfeucht game decision procedure.- Some additional upper bounds.- Direct products of theories.- Lower bound preliminaries.- A technique for writing short formulas defining complicated properties.- A lower bound on the theories of pairing functions.- Some additional lower bounds.

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