21 citations · 55 across the 14 of their papers we have counts for
10 papers · 1 filter
On simple groups definable in some valued fields
Jakub Gismatullin, Immanuel Halupczok, Dugald Macpherson
We prove that non-abelian definable, definably simple groups in 1-h-minimal henselian valued fields are essentially already linear algebraic groups. Here, the group is assumed to l…
On binomials and algebraic closure of some pseudofinite fields
Jakub Gismatullin, Katarzyna Tarasek
We give a criterion when a polynomial is irreducible over a pseudofinite field. As an application we give an explicit description of algebraic closure of some pseudofinite…
Bohr compactifications of groups and rings
Jakub Gismatullin, Grzegorz Jagiella, Krzysztof Krupinski
We introduce and study model-theoretic connected components of rings as an analogue of model-theoretic connected components of definable groups. We develop their basic theory and u…
On compactifications and the topological dynamics of definable groups
Jakub Gismatullin, Davide Penazzi, Anand Pillay
We discuss definable compactifications and topological dynamics. For G a group definable in some structure M, we define notions of "definable" compactification of G and "definable"…
Some model theory of SL(2,R)
Jakub Gismatullin, Davide Penazzi, Anand Pillay
We study the action of G = SL(2,R) on its type space S_G(R) where R denotes the field of real numbers. We identify a minimal closed G-flow I, and an idempotent r of I (with the res…
On model-theoretic connected components in some group extensions
Jakub Gismatullin, Krzysztof Krupinski
We analyze model-theoretic connected components in extensions of a given group by abelian groups which are defined by means of 2-cocycles with finite image. We characterize, in ter…