On the existence of kappa-existentially closed groups

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 cardinalityκ for regular κ with 2^{<κ} = κ. Moreover, we prove that there exists noκ-existentially closed group of cardinality κ for singular κ. Assuming thegeneralized continuum hypothesis, we completely determine the cardinalsκ ≤ λ for which a κ-existentially closed group of cardinality λ exists


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Citation Formats
O. H. Kegel, B. Kaya, and M. Kuzucuoğlu, “On the existence of kappa-existentially closed groups,” ARCHIV DER MATHEMATIK, pp. 225–229, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/37032.