Kelley's specialization of Tychonoff's Theorem is equivalent to the Boolean Prime Ideal Theorem

Eric Schechter

doi:10.4064/fm189-3-5

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Kelley's specialization of Tychonoff's Theorem is equivalent to the Boolean Prime Ideal Theorem

Eric Schechter

Year: 2006 Journal: Fundamenta Mathematicae Vol: 189 (3)Pages: 285-288 Publisher: Polish Academy of Sciences

DOI: 10.4064/fm189-3-5

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Abstract

The principle that “any product of cofinite topologies is compact” is equivalent (without appealing to the Axiom of Choice) to the Boolean Prime Ideal Theorem.

Keywords:

Mathematics Boolean prime ideal theorem Axiom of choice Ideal (ethics) Stone's representation theorem for Boolean algebras Discrete mathematics Prime (order theory) Pure mathematics Combinatorics Algebra over a field Two-element Boolean algebra Set (abstract data type) Set theory

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Advanced Topology and Set Theory

Physical Sciences → Mathematics → Geometry and Topology

Mathematical and Theoretical Analysis

Physical Sciences → Mathematics → Mathematical Physics

Advanced Algebra and Logic

Physical Sciences → Computer Science → Computational Theory and Mathematics

Kelley's specialization of Tychonoff's Theorem is equivalent to the Boolean Prime Ideal Theorem

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