Burak Kaya

E-mail

burakk@metu.edu.tr

Department

Department of Mathematics

ORCID

0000-0002-9318-5360

Scopus Author ID

57193827867

Web of Science Researcher ID

AAS-5827-2020

Limit groups and automorphisms of κ-existentially closed groups Kaya, Burak; Kuzucuoğlu, Mahmut; Longobardi, Patrizia; Maj, Mercede (2025-03-15) The structure of automorphism groups of κ-existentially closed groups has been studied by Kaya-Kuzucuoğlu in 2022. It was proved that Aut(G) is the union of subgroups of level preserving automorphisms and |Aut(G)|=2κ whene...
EXISTENTIALLY AND κ-EXISTENTIALLY CLOSED GROUPS Kaya, Burak; Kuzucuoğlu, Mahmut (2023-03-01) A group G is existentially closed (algebraically closed) if every finite system of equations and in-equations that has coefficients in G and has a solution in an overgroup H ≥ G has a solution in G. Existentially closed gr...
Descriptive complexity of subsets of the space of finitely generated groups Benli, Mustafa Gökhan; Kaya, Burak (2022-12-01) © 2022 Elsevier GmbHIn this paper, we determine the descriptive complexity of subsets of the Polish space of marked groups defined by various group theoretic properties. In particular, using Grigorchuk groups, we establish...
Automorphisms of κ -existentially closed groups Kaya, Burak; Kuzucuoğlu, Mahmut (2022-08-01) We investigate the automorphisms of some κ-existentially closed groups. In particular, we prove that Aut(G) is the union of subgroups of level preserving automorphisms and | Aut(G) | = 2 κ whenever κ is inaccessible and G ...
On the closed Ramsey numbers R-cl(omega plus n, 3) Kaya, Burak (2021-11-01) In this paper, we contribute to the study of topological partition relations for pairs of countable ordinals and prove that, for all integers n ≥ 3, Rcl(ω + n, 3) ≥ ω2 · n + ω · (R(n, 3) − n) + n, Rcl(ω + n, 3) ≤ ω2 · n +...
On the existence of kappa-existentially closed groups Kegel, Otto H.; Kaya, Burak; Kuzucuoğlu, Mahmut (2018-09-01) We prove that a κ-existentially closed group of cardinality λ exists whenever κ ≤ λ are uncountable cardinals with λ^{<κ} = λ. In particular, we show that there exists a κ-existentially closed group of cardinalityκ for ...
THE COMPLEXITY OF THE TOPOLOGICAL CONJUGACY PROBLEM FOR TOEPLITZ SUBSHIFTS Kaya, Burak (2017-06-01) In this paper, we analyze the Borel complexity of the topological conjugacy relation on Toeplitz subshifts. More specifically, we prove that topological conjugacy of Toeplitz subshifts with separated holes is hyperfinite. ...
The complexity of topological conjugacy of pointed Cantor minimal systems Kaya, Burak (2017-05-01) In this paper, we analyze the complexity of topological conjugacy of pointed Cantor minimal systems from the point of view of descriptive set theory. We prove that the topological conjugacy relation on pointed Cantor minim...

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