Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 44, Number 3 (2003), 175-184.
On Sequentially Compact Subspaces of without the Axiom of Choice
We show that the property of sequential compactness for subspaces of is countably productive in ZF. Also, in the language of weak choice principles, we give a list of characterizations of the topological statement 'sequentially compact subspaces of are compact'. Furthermore, we show that forms 152 (= every non-well-orderable set is the union of a pairwise disjoint well-orderable family of denumerable sets) and 214 (= for every family A of infinite sets there is a function f such that for all y∊ A, f(y) is a nonempty subset of y and ∣ f(y) ∣ = א₀) of Howard and Rubin are equivalent.
Notre Dame J. Formal Logic, Volume 44, Number 3 (2003), 175-184.
First available in Project Euclid: 28 July 2004
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Keremedis, Kyriakos; Tachtsis, Eleftherios. On Sequentially Compact Subspaces of without the Axiom of Choice. Notre Dame J. Formal Logic 44 (2003), no. 3, 175--184. doi:10.1305/ndjfl/1091030855. https://projecteuclid.org/euclid.ndjfl/1091030855