5 citations · 16 across the 17 of their papers we have counts for
18 papers
Ramsey theory and topological dynamics of 0-dimensional flows
Krzysztof Krupiński, Junguk Lee, Slavko Moconja
We introduce several Ramsey-theoretic properties of 0-dimensional ambits and obtain their dynamical characterizations. In consequence, we obtain Ramsey-theoretic criteria for trivi…
The Ax-Kochen-Ershov principles via the higher valued hyperfield
Junguk Lee
In this paper, we concern the model theory of finitely ramified henselian valued fields via higher valued hyperfields. Most of all, we provide a number of Ax-Kochen-Ershov Theorems…
Relativized Galois groups of first order theories over a hyperimaginary
Hyoyoon Lee, Junguk Lee
We study relativized Lascar groups, which are formed by relativizing Lascar groups to the solution set of a partial type . We introduce the notion of a Lascar tuple for and…
Preservation of NATP
JinHoo Ahn, Joonhee Kim, Hyoyoon Lee +1
We prove several preservation theorems for NATP and furnish several examples of NATP. First, we prove preservation of NATP for the parametrization and sum of the theories of Fraïss…
On the Antichain Tree Property
JinHoo Ahn, Joonhee Kim, Junguk Lee
In this note, we investigate a new model theoretical tree property, called the antichain tree property (ATP). We develop combinatorial techniques for ATP. First, we show that ATP i…
The embedding property for sorted profinite groups
Junguk Lee
We study the embedding property in the category of sorted profinite groups. We introduce a notion of the sorted embedding property (SEP), analogous to the embedding property for pr…
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.
Ramsey theory and topological dynamics for first order theories
Krzysztof Krupinski, Junguk Lee, Slavko Moconja
We investigate interactions between Ramsey theory, topological dynamics, and model theory. We introduce various Ramsey-like properties for first order theories and characterize the…
Co-theory of sorted profinite groups for PAC structures
Daniel Max Hoffmann, Junguk Lee
We achieve several results. First, we develop a variant of the theory of absolute Galois groups in the context of many sorted structures. Second, we provide a method for coding abs…
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…
Hyperfields, truncated DVRs and valued fields
Junguk Lee
For any two complete discrete valued fields and of mixed characteristic with perfect residue fields, we show that if the -th valued hyperfields of and ar…
Geometric stability theory for -structures
Junguk Lee, Michael Cohen, Phillip Wesolek
We introduce a notion of -structures which are certain locally compact group actions and prove some counterparts of results on Polish structures(introduced by Krupinski in \cite…
On the structure of certain valued fields
Junguk Lee, Wan Lee
In this article, we study the structure of finitely ramified mixed characteristic valued fields. For any two complete discrete valued fields and of mixed characteristic…
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…
Some arithmetic properties on nonstandard rationals
Junguk Lee
For a given number field , we show that the ranks of nonsingular elliptic curves over are uniformly finitely bounded if and only if weak Mordell-Weil property holds in all(s…
Non-commutative groupoids obtained from the failure of -uniqueness in stable theories
Byunghan Kim, SunYoung Kim, Junguk Lee
We construct a possibly non-commutative groupoid from the failure of -uniqueness of a strong type. The commutative groupoid constructed by John Goodrick and Alexei Kolesnikov in…
Lascar groups and the first homology groups of strong types in rosy theories
Junguk Lee
For a rosy theory, we give a canonical surjective homomorphism from a Lascar group over $A=\acl^{eq}(A)$ to a first homology group of a strong type over , and we describe its ke…
A classification of 2-chains having 1-shell boundaries in rosy theories
Byunghan Kim, SunYoung Kim, Junguk Lee
We classify, in a non-trivial amenable collection of functors, all 2-chains up to the relation of having the same 1-shell boundary. In particular, we prove that in a rosy theory, e…