19 citations · 34 across the 10 of their papers we have counts for
10 papers
Upside down and backwards
Kyle Gannon, Tomasz Rzepecki
We investigate the semigroup of invariant types through the lens of Ellis theory; primarily focusing on definably amenable NIP groups. In this context, we observe that the collecti…
Homogeneity of abstract linear spaces
Wiesław Kubiś, Piotr Nowakowski, Tomasz Rzepecki
We discuss homogeneity and universality issues in the theory of abstract linear spaces, namely, structures with points and lines satisfying natural axioms, as in Euclidean or proje…
Generating ideals by additive subgroups of rings
Krzysztof Krupiński, Tomasz Rzepecki
We obtain several fundamental results on finite index ideals and additive subgroups of rings as well as on model-theoretic connected components of rings, which concern generating i…
On the automorphism group of the universal homogeneous meet-tree
Itay Kaplan, Tomasz Rzepecki, Daoud Siniora
We show that the countable universal homogeneous meet-tree has a generic automorphism, but it does not have a generic pair of automorphisms.
Hereditary G-compactness
Tomasz Rzepecki
We introduce the notion of hereditary G-compactness (with respect to interpretation). We provide a sufficient condition for a poset to not be hereditarily G-compact, which we use t…
Bounded Invariant Equivalence Relations
Tomasz Rzepecki
We study strong types and Galois groups in model theory from a topological and descriptive-set-theoretical point of view, leaning heavily on topological dynamical tools. More preci…
Galois groups as quotients of Polish groups
Krzysztof Krupiński, Tomasz Rzepecki
We present the (Lascar) Galois group of any countable theory as a quotient of a compact Polish group by an normal subgroup: in general, as a topological group, and under NIP,…
Equivalence relations invariant under group actions
Tomasz Rzepecki
We extend some recent results about bounded invariant equivalence relations and invariant subgroups of definable groups: we show that type-definability and smoothness are equivalen…
Topological dynamics and the complexity of strong types
Krzysztof Krupiński, Anand Pillay, Tomasz Rzepecki
We develop topological dynamics for the group of automorphisms of a monster model of any given theory. In particular, we find strong relationships between objects from topological…
Smoothness of bounded invariant equivalence relations
Krzysztof Krupiński, Tomasz Rzepecki
We generalise the main theorems from the paper "The Borel cardinality of Lascar strong types" by I. Kaplan, B. Miller and P. Simon to a wider class of bounded invariant equivalence…