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On the existence of kappa-existentially closed groups
Download
10.1007s00013-018-1213-x.pdf
Date
2018-09-01
Author
Kaya, Burak
Kegel, Otto H.
Kuzucuoğlu, Mahmut
Metadata
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This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
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We prove that a κ-existentially closed group of cardinality λ exists whenever κ ≤ λ are uncountable cardinals with λ^{<κ} = λ. In particular, we show that there exists a κ-existentially closed group of cardinality κ for regular κ with 2^{<κ} = κ. Moreover, we prove that there exists no κ-existentially closed group of cardinality κ for singular κ. Assuming the generalized continuum hypothesis, we completely determine the cardinals κ ≤ λ for which a κ-existentially closed group of cardinality λ exists<br>
Subject Keywords
Existentially closed groups
,
Homogeneous groups
,
Infinite symmetric groups
URI
https://hdl.handle.net/11511/37032
Journal
ARCHIV DER MATHEMATIK
DOI
https://doi.org/10.1007/s00013-018-1213-x
Collections
Department of Mathematics, Article