Boolean sentence algebras: Isomorphism constructions

Journal of Symbolic Logic 48 (2):329-338 (1983)
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Abstract

Associated with each first-order theory is a Boolean algebra of sentences and a Boolean space of models. Homomorphisms between the sentence algebras correspond to continuous maps between the model spaces. To what do recursive homomorphisms correspond? We introduce axiomatizable maps as the appropriate dual. For these maps we prove a Cantor-Bernstein theorem. Duality and the Cantor-Bernstein theorem are used to show that the Boolean sentence algebras of any two undecidable languages or of any two functional languages are recursively isomorphic where a language is undecidable iff it has at least one operation or relation symbol of two or more places or at least two unary operation symbols, and a language is functional iff it has exactly one unary operation symbol and all other symbols are for unary relations, constants, or propositions

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Citations of this work

The Boolean algebra of formulas of first-order logic.Don H. Faust - 1982 - Annals of Mathematical Logic 23 (1):27.

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References found in this work

Models and Ultraproducts: An Introduction.J. L. Bell & A. B. Slomson - 1972 - Journal of Symbolic Logic 37 (4):763-764.
Introduction to Mathematical Logic.D. van Dalen - 1964 - Journal of Symbolic Logic 45 (3):631-631.
Cylindric Algebras.Leon Henkin & Alfred Tarski - 1967 - Journal of Symbolic Logic 32 (3):415-416.
Annals of Mathematical Logic: Announcement of a New Periodical.[author unknown] - 1969 - Journal of Symbolic Logic 34 (3):532-532.

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