Notre Dame Journal of Formal Logic

On Sequentially Compact Subspaces of 𝕉 without the Axiom of Choice

Kyriakos Keremedis and Eleftherios Tachtsis

Abstract

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 yA, f(y) is a nonempty subset of y and ∣ f(y) ∣ = א₀) of Howard and Rubin are equivalent.

Article information

Source
Notre Dame J. Formal Logic, Volume 44, Number 3 (2003), 175-184.

Dates
First available in Project Euclid: 28 July 2004

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1091030855

Digital Object Identifier
doi:10.1305/ndjfl/1091030855

Mathematical Reviews number (MathSciNet)
MR2130789

Zentralblatt MATH identifier
1071.03035

Subjects
Primary: 54D30: Compactness 54D55: Sequential spaces 54D20: Noncompact covering properties (paracompact, Lindelöf, etc.)

Keywords
weak forms of the axiom of choice compactness sequential compactness Tychonoff product

Citation

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


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References

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