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COUNTABLY COMPACT EXTENSIONS AND CARDINAL CHARACTERISTICS OF THE CONTINUUM

Part of: Fairly general properties Generalities Set theory

Published online by Cambridge University Press:  13 February 2025

SERHII BARDYLA Open the ORCID record for SERHII BARDYLA [Opens in a new window] ,
PETER NYIKOS  and
LYUBOMYR ZDOMSKYY Open the ORCID record for LYUBOMYR ZDOMSKYY [Opens in a new window]
SERHII BARDYLA*
Affiliation:
FACULTY OF MATHEMATICS UNIVERSITY OF VIENNA VIENNA, AUSTRIA URL: http://www.logic.univie.ac.at/~bardylas55/
PETER NYIKOS
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF SOUTH CAROLINA COLUMBIA, SC, USA E-mail [email protected] URL: https://people.math.sc.edu/nyikos/
LYUBOMYR ZDOMSKYY
Affiliation:
INSTITUTE OF DISCRETE MATHEMATICS AND GEOMETRY VIENNA UNIVERSITY OF TECHNOLOGY (TU WIEN) VIENNA, AUSTRIA E-mail [email protected] URL: https://dmg.tuwien.ac.at/zdomskyy/
*
E-mail: [email protected]
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Abstract

In this paper, we show that the existence of certain first-countable compact-like extensions is equivalent to the equality between corresponding cardinal characteristics of the continuum. For instance, $\mathfrak b=\mathfrak s=\mathfrak c$ if and only if every regular first-countable space of weight $< \mathfrak c$ can be densely embedded into a regular first-countable countably compact space.

Keywords

Nyikos spacecountably compactpseudocompactembeddingcardinal characteristics of the continuum

MSC classification

Primary: 54A35: Consistency and independence results 54D35: Extensions of spaces (compactifications, supercompactifications, completions, etc.) 03E17: Cardinal characteristics of the continuum
Type
Article
Information
The Journal of Symbolic Logic , First View , pp. 1 - 27
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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Footnotes

Sadly, Peter Nyikos passed away in February 2024, when this work was in the final stage of the preparation. Therefore the rest of the authors decided to finish the research and to submit the paper with his name as coauthor. This is our tribute to our dear friend Peter.

References

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