The Boolean algebra of formulas of first-order logic

Abstract

The algebraic and recursive structure of countable languages of classical first-order logic with equality is analysed. All languages of finite undecidable similarity type are shown to be algebraically and recursively equivalent in the following sense: their Boolean algebras of formulas are, after trivial involving the one element models of the languages have been excepted, recursively isomorphic by a map which preserves the degree of recursiveness of their models.