Kelley's specialization of Tychonoff's Theorem is equivalent to the Boolean Prime Ideal Theorem
Fundamenta Mathematicae, Tome 189 (2006) no. 3, pp. 285-288.

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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.
DOI : 10.4064/fm189-3-5
Keywords: principle product cofinite topologies compact equivalent without appealing axiom choice boolean prime ideal theorem

Eric Schechter 1

1 Department of Mathematics Vanderbilt University 1326 Stevenson Center Nashville, TN 37240, U.S.A.
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Eric Schechter. Kelley's specialization of Tychonoff's Theorem
 is equivalent to the Boolean Prime Ideal Theorem. Fundamenta Mathematicae, Tome 189 (2006) no. 3, pp. 285-288. doi : 10.4064/fm189-3-5. http://geodesic.mathdoc.fr/articles/10.4064/fm189-3-5/

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