The Boolean algebra of formulas of first-order logic

Annals of Mathematical Logic 23 (1):27 (1982)
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Abstract

The algebraic 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 factors 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

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References found in this work

Model-theoretic methods in the study of elementary logic.William Hanf - 1965 - Journal of Symbolic Logic 34 (1):132--145.
Effectively extensible theories.Marian Boykan Pour-El - 1968 - Journal of Symbolic Logic 33 (1):56-68.

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