3 papers
math.LO2024
Generic groups and the weak amalgamation property
Aleksander Ivanov, Krzysztof Majcher
We consider the logic space of countable (enumerated) groups and show that closed subspaces corresponding to some standard classes of groups have (do not have) generic groups. We a…
math.GR2020
Metric ultraproducts of groups -- simplicity, perfectness and torsion
Jakub Gismatullin, Krzysztof Majcher, Martin Ziegler
We characterise the simplicity of metric ultraproducts of a family of metric groups. We also present several new examples of simple groups, such as metric ultraproducts of finite a…
math.LO2006
Nice enumerations of omega-categorical groups
A. Ivanov, K. Majcher
We give an example of an omega-categorical group without AZ-enumerations. We build AZ-enumerations of some omega-categorical central products of countably many copies of a finite 2…