Countable products and countable direct sums of compact metrizable spaces in the absence of the Axiom of Choice
From MaRDI portal
Publication:6040620
DOI10.1016/j.apal.2023.103283arXiv2109.00640OpenAlexW4367317494MaRDI QIDQ6040620
Kyriakos Keremedis, Eliza Wajch, Eleftherios Tachtsis
Publication date: 19 May 2023
Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2109.00640
countable productcompact metrizable spaceFraenkel-Mostowski modelscountable direct sum\(ZF\)-modelsweak forms of the Axiom of Choice
Compactness (54D30) Metric spaces, metrizability (54E35) Consistency and independence results (03E35) Product spaces in general topology (54B10) Consistency and independence results in general topology (54A35) Axiom of choice and related propositions (03E25)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On Loeb and sequential spaces in \textbf{ZF}
- Set theory. An introduction to independence proofs. 2nd print
- Infinite permutation groups. II: Subgroups of small index
- Disasters in topology without the axiom of choice
- Quasi-metrizability of products in ZF and equivalences of CUT(fin)
- Continuing horrors of topology without choice
- Second-countable compact Hausdorff spaces as remainders in \textbf{ZF} and two new notions of infiniteness
- Several results on compact metrizable spaces in \(\mathbf{ZF} \)
- Some independence results about compact metrizable spaces and two notions of finiteness
- On metrizability and compactness of certain products without the axiom of choice
- Stranger things about the cardinality of compact metric spaces without AC
- Cuf products and cuf sums of (quasi-) metrizable spaces in ZF
- Compact Metric Spaces and Weak Forms of the Axiom of Choice
- Some Notions of Separability of Metric Spaces in $\mathbf {ZF}$ and Their Relation to Compactness
- Countable sums and products of metrizable spaces in ZF
- The Algebraic Simplicity of Certain Groups of Homeomorphisms
- SUBGROUPS OF SMALL INDEX IN ORDERED PERMUTATION GROUPS
- Countable Compact Scattered T2Spaces and Weak Forms of AC
- Unions and the axiom of choice
- Products of Compact Spaces in the Least Permutation Model
- Models of set theory containing many perfect sets
- Limitations on the Fraenkel-Mostowski method of independence proofs
- Metric spaces and the axiom of choice
- Consequences of the failure of the axiom of choice in the theory of Lindelöf metric spaces
- Set Theory
- A New Proof of the Tychonoff Theorem
- Zermelo-Fraenkel consistency results by Fraenkel-Mostowski methods
- The Tychonoff product theorem implies the axiom of choice
- Axiom of choice
- The axiom of choice