On the existence of kappa-existentially closed groups
ARCHIV DER MATHEMATIK, cilt.111, ss.225-229, 2018 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 111
- Basım Tarihi: 2018
- Doi Numarası: 10.1007/s00013-018-1213-x
- Dergi Adı: ARCHIV DER MATHEMATIK
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.225-229
- Anahtar Kelimeler: Existentially closed groups, Infinite symmetric groups, Homogeneous groups
- Orta Doğu Teknik Üniversitesi Adresli: Evet
Özet
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