Preservation under Extensions on Well-Behaved Finite Structures
β Scribed by Atserias, Albert; Dawar, Anuj; Grohe, Martin
- Book ID
- 118180753
- Publisher
- Society for Industrial and Applied Mathematics
- Year
- 2008
- Tongue
- English
- Weight
- 229 KB
- Volume
- 38
- Category
- Article
- ISSN
- 0097-5397
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## Abstract We characterize preservation of superstability and Οβstability for finite extensions of abelian groups and reduce the general case to the case of __p__βgroups. In particular we study finite extensions of divisible abelian groups. We prove that superstable abelianβbyβfinite groups have o
A congruence Ο T on a subsemigroup T of S extends to the semigroup S, if there exists a congruence Ο on S such that Ο T = Ο T . A semigroup S has the congruence extension property (CEP) if each congruence on each subsemigroup extends to S. Previously, it was shown that a semigroup S has CEP if and o