Martin-Pizarro, Amador Palacín, Daniel Wolf, Julia
Published in
Selecta Mathematica

A non-quantitative version of the Freiman–Ruzsa theorem is obtained for finite stable sets with small tripling in arbitrary groups, as well as for (finite) weakly normal subsets in abelian groups.

Kikyo, Hirotaka

The automorphism groups of Hrushovski's pseudoplanes associated to rational numbers α with 1/3 >α≥1/4 are simple groups.

Andréka, Hajnal Németi, István
Published in
Algebra universalis

We prove that persistently finite algebras are not created by completions of algebras, in any ordered discriminator variety. A persistently finite algebra is one without infinite simple extensions. We prove that finite measurable relation algebras are all persistently finite. An application of these theorems is that the variety generated by the com...

KIKYO, HIROTAKA

The automorphism group of Hrushovski's pseudoplane associated to 5/8 is a simple group.

Kikyo, Hirotaka

Hrushovski's pseudoplane associated to rational number 5/8 has a model complete theory.

Kikyo, Hirotaka
Published in
Archive for Mathematical Logic

Let Kf\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {K}_f$$\end{document} be an ab initio amalgamation class with an unbounded increasing concave function f. ...

Macpherson, Dugald
Published in
Archive for Mathematical Logic

This is a survey, intended both for group theorists and model theorists, concerning the structure of pseudofinite groups, that is, infinite models of the first-order theory of finite groups. The focus is on concepts from stability theory and generalisations in the context of pseudofinite groups, and on the information this might provide for finite ...

Wires, Alexander
Published in
Annals of Combinatorics

For simple graphs, we investigate and seek to characterize the properties first-order definable by the induced subgraph relation. Let PG\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \b...

Jasiński, Jakub
Published in
Combinatorica

We investigate the combinatorial properties of the Fraïssé class of structures induced by the leaf sets of boron trees — graph-theoretic binary trees without an assigned root — and compute their Ramsey degrees. The Ramsey degree of a boron tree structure is shown to equal the number of its possible orientations, which are herein defined to depend o...

Kubiś, Wiesław
Published in
Forum Mathematicum

We present a purely category-theoretic characterization of retracts of Fraïssé limits. For this aim, we consider a natural version of injectivity with respect to a pair of categories (a category and its subcategory). It turns out that retracts of Fraïssé limits are precisely the objects that are injective relatively to such a pair. One of the appli...