On the existence of kappa-existentially closed groups
ARCHIV DER MATHEMATIK, vol.111, pp.225-229, 2018 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 111
- Publication Date: 2018
- Doi Number: 10.1007/s00013-018-1213-x
- Journal Name: ARCHIV DER MATHEMATIK
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.225-229
- Keywords: Existentially closed groups, Infinite symmetric groups, Homogeneous groups
- Middle East Technical University Affiliated: Yes
Abstract
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