15 citations · 50 across the 19 of their papers we have counts for
22 papers
Automorphisms of valued fields: amalgamation and existential closedness
Jan Dobrowolski, Francesco Gallinaro, Rosario Mennuni
We study valued fields equipped with an automorphism. We prove that all of them have an extension admitting an equivariant cross-section of the valuation. In residual characteristi…
Fields with Lie-commuting and iterative operators
Jan Dobrowolski, Omar Leon Sanchez
We introduce a general framework for studying fields equipped with operators, given as co-ordinate functions of homomorphisms into a local algebra , satisfying various…
Corrigendum to "Kim-independence in positive logic"
Jan Dobrowolski, Mark Kamsma
The proof of the Independence Theorem for Kim-independence in positive thick NSOP theories from (Dobrowolski and Kamsma, 2022) contains a gap. The theorem is still true, and in…
Elekes-Szabó for collinearity on cubic surfaces
Martin Bays, Jan Dobrowolski, Tingxiang Zou
We study the orchard problem on cubic surfaces. We classify possibly reducible cubic surfaces $X\subseteq \mathbb{P}^3(\C)$ with smooth components on which there exist families of…
The Amalgamation Property for automorphisms of ordered abelian groups
Jan Dobrowolski, Rosario Mennuni
We prove that the category of ordered abelian groups equipped with an automorphism has the Amalgamation Property, deduce that their inductive theory is NIP in the sense of positive…
On rank not only in NSOP1 theories
Jan Dobrowolski, Daniel Max Hoffmann
We introduce a family of local ranks DQ depending on a finite set Q of pairs of the form (φ(x,y),q(y)) where φ(x,y) is a formula and q(y) is a global type. We prove that in any NSO…
Elekes-Szabó for groups, and approximate subgroups in weak general position
Martin Bays, Jan Dobrowolski, Tingxiang Zou
We show that with a suitable weak notion of general position, the Elekes-Szabó condition on the group operation of a connected complex algebraic group characterises nilpotence of t…
Kim-independence in positive logic
Jan Dobrowolski, Mark Kamsma
An important dividing line in the class of unstable theories is being NSOP, which is more general than being simple. In NSOP theories forking independence may not be as wel…
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.
Sets, groups, and fields definable in vector spaces with a bilinear form
Jan Dobrowolski
We study definable sets, groups, and fields in the theory of infinite-dimensional vector spaces over an algebraically closed field equipped with a nondegenerate symmetri…
Independence over arbitrary sets in NSOP theories
Jan Dobrowolski, Byunghan Kim, Nicholas Ramsey
We study Kim-independence over arbitrary sets. Assuming that forking satisfies existence, we establish Kim's lemma for Kim-dividing over arbitrary sets in an NSOP theory. We…
Elementary Equivalence Theorem for PAC structures
Jan Dobrowolski, Daniel Max Hoffmann, Junguk Lee
We generalize a well-known theorem binding the elementary equivalence relation on the level of PAC fields and the isomorphism class of their absolute Galois groups. Our results con…
On omega-categorical groups and rings of finite burden
Frank Olaf Wagner, Jan Dobrowolski
An -categorical group of finite burden is virtually finite-by-abelian; an -categorical ring of finite burden is virtually finite-by-null; an -categorical NTP2 ring is virt…
Valuation theory, generalized IFS attractors and fractals
Jan Dobrowolski, Franz-Viktor Kuhlmann
Using valuation rings and valued fields as examples, we discuss in which ways the notions of "topological IFS attractor" and "fractal space" can be generalized to cover more genera…
A preservation theorem for theories without the tree property of the first kind
Jan Dobrowolski, Hyeungjoon Kim
We prove that the NTP property of a geometric theory is inherited by theories of lovely pairs and -structures associated to . We also provide a class of examples of n…
Left-ordered inp-minimal groups
Jan Dobrowolski, John Goodrick
We prove that any left-ordered inp-minimal group is abelian, and we provide an example of a non-abelian left-ordered group of dp-rank 2.
The Lascar groups and the 1st homology groups in model theory
Jan Dobrowolski, Byunghan Kim, Junguk Lee
Let be a strong type of an algebraically closed tuple over $B=\acl^{\eq}(B)$ in any theory . Depending on a ternary relation $\indo^*$ satisfying some basic axioms (there is…
Topologies induced by group actions
Jan Dobrowolski
We introduce some canonical topologies induced by actions of topological groups on groups and rings. For being a group [or a ring] and a topological group acting on as…
Locally finite profinite rings
Jan Dobrowolski, Krzysztof Krupiński
We investigate the structure of locally finite profinite rings. We classify (Jacobson-) semisimple locally finite profinite rings as products of complete matrix rings of bounded ca…
New examples of small Polish structures
Jan Dobrowolski
We answer some questions from a paper of Krupiński by giving suitable examples of small Polish structures. First, we present a class of small Polish group structures without generi…
On ω-categorical, generically stable groups and rings
Jan Dobrowolski, Krzysztof Krupinski
We prove that every ω-categorical, generically stable group is nilpotent-by-finite and that every ω-categorical, generically stable ring is nilpotent-by-finite.
On ω-categorical, generically stable groups
Jan Dobrowolski, Krzysztof Krupinski
We prove that each ω-categorical, generically stable group is solvable-by-finite.