40 citations · 64 across the 6 of their papers we have counts for
8 papers · 1 filter
The relativized Lascar groups, type-amalgamation, and algebraicity
Jan Dobrowolski, Byunghan Kim, Alexei Kolesnikov +1
We apply compact group theory to obtain some model-theoretic results about the relativized Lascar Galois group of a strong type.
Homology groups of types in stable theories and the Hurewicz correspondence
John Goodrick, Byunghan Kim, Alexei Kolesnikov
We give an explicit description of the homomorphism group H_n(p) of a strong type p in any stable theory under the assumption that for every non-forking extension q of p the groups…
The Hanf number for amalgamation of coloring classes
Alexei Kolesnikov, Chris Lambie-Hanson
We study amalgamation properties in a family of abstract elementary classes that we call coloring classes. The family includes the examples previously studied in previous work of B…
Type-amalgamation properties and polygroupoids in stable theories
John Goodrick, Byunghan Kim, Alexei Kolesnikov
We show that in a stable first-order theory, the failure of higher-dimensional type amalgamation can always be witnessed by algebraic structures which we call n-ary polygroupoids.…
Canonical forking in AECs
Will Boney, Rami Grossberg, Alexei Kolesnikov +1
Boney and Grossberg [BG] proved that every nice AEC has an independence relation. We prove that this relation is unique: In any given AEC, there can exist at most one independence…
Amalgamation functors and homology groups in model theory
John Goodrick, Byunghan Kim, Alexei Kolesnikov
We present definitions of homology groups associated to a family of amalgamation functors. We show that if the generalized amalgamation properties hold, then the homology groups ar…