Existentially Closed Closure Algebras

Notre Dame Journal of Formal Logic 61 (4):623-661 (2020)
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Abstract

The study of existentially closed closure algebras begins with Lipparini’s 1982 paper. After presenting new nonelementary axioms for algebraically closed and existentially closed closure algebras and showing that these nonelementary classes are different, this paper shows that the classes of finitely generic and infinitely generic closure algebras are closed under finite products and bounded Boolean powers, extends part of Hausdorff’s theory of reducible sets to existentially closed closure algebras, and shows that finitely generic and infinitely generic closure algebras are elementarily inequivalent. Special properties of algebraically closed, existentially closed, finitely generic, and infinitely generic closure algebras are established along the way.

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Citations of this work

A Model Theory of Topology.Paolo Lipparini - forthcoming - Studia Logica:1-35.

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References found in this work

The Algebra of Topology.J. C. C. Mckinsey & Alfred Tarski - 1944 - Annals of Mathematics, Second Series 45:141-191.
On Closed Elements in Closure Algebras.J. C. C. Mckinsey & Alfred Tarski - 1946 - Annals of Mathematics, Ser. 2 47:122-162.
Model existence theorems for modal and intuitionistic logics.Melvin Fitting - 1973 - Journal of Symbolic Logic 38 (4):613-627.

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