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November 2020 Existentially Closed Closure Algebras
Philip Scowcroft
Notre Dame J. Formal Logic 61(4): 623-661 (November 2020). DOI: 10.1215/00294527-2020-0026

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 (a.c.), existentially closed (e.c.), finitely generic (f.g.), and infinitely generic (i.g.) closure algebras are established along the way.

Citation

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Philip Scowcroft. "Existentially Closed Closure Algebras." Notre Dame J. Formal Logic 61 (4) 623 - 661, November 2020. https://doi.org/10.1215/00294527-2020-0026

Information

Received: 24 January 2020; Accepted: 9 September 2020; Published: November 2020
First available in Project Euclid: 29 December 2020

Digital Object Identifier: 10.1215/00294527-2020-0026

Subjects:
Primary: 03C60
Secondary: 03C25, 06E25

Rights: Copyright © 2020 University of Notre Dame

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Vol.61 • No. 4 • November 2020
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