Related papers: Structural Ramsey Theory and the Extension Propert…
The class of finite distributive lattices, as many other classes of structures in everyday use, does not have the Ramsey property. It is quite common, though, that after expanding the structures with appropriatelly chosen linear orders the…
We extend the Kechris--Pestov--Todor\v{c}evi\'c correspondence to weak Fra\"{\i}ss\'{e} categories and automorphism groups of generic objects. The new ingredient is the weak Ramsey property. We demonstrate the theory on several examples…
In 2003, Kechris, Pestov and Todorcevic showed that the structure of certain separable metric spaces - called ultrahomogeneous - is closely related to the combinatorial behavior of the class of their finite metric spaces. The purpose of the…
We study Ramsey-theoretic properties of several natural classes of finite ultrametric spaces, describe the corresponding Urysohn spaces and compute a dynamical invariant attached to their isometry groups.
We give an abstract approach to finite Ramsey theory and prove a general Ramsey-type theorem. We deduce from it a self-dual Ramsey theorem, which is a new result naturally generalizing both the classical Ramsey theorem and the dual Ramsey…
This is Part II of a two-part series regarding Ramsey properties of Fraisse structures satisfying a property called SDAP+, which strengthens the Disjoint Amalgamation Property. In Part I, we prove that every Fraisse structure in a finite…
Big Ramsey degrees of finite structures are usually considered with respect to a Fra\"{i} ss\'e limit. Building mainly on the work of Devlin, Sauer, Laflamme and Van Th\'e, in this paper we consider structures which are not Fra\"{i} ss\'e…
We give simple characterizations of the category PAsm(A) of partitioned assemblies, and of the realizability topos RT(A) over a partial combinatory algebra A. This answers the question for an 'extensional characterization' of realizability…
The paper is devoted to a study of certain fixed point properties, and their relatives, in the context of full automorphism groups of countable rooted trees. Namely, we study Serre's property (FA'), also called unsplittability, property…
We formulate a property strengthening the Disjoint Amalgamation Property and prove that every Fraisse structure in a finite relational language with relation symbols of arity at most two having this property has finite big Ramsey degrees…
The class of finite distributive lattices, as many other classes of structures, does not have the Ramsey property. It is quite common, though, that after expanding the structures with appropriately chosen linear orders the resulting class…
We extend the notions of "$R_\infty$-property" and "full (extended) Reidemeister spectrum" to finite groups in a meaningful way. We provide examples of finite groups admitting these properties, if they exist, by looking at groups of small…
We study the preservation of certain properties under products of classes of finite structures. In particular, we examine indivisibility, definable self-similarity, the amalgamation property, and the disjoint n-amalgamation property. We…
We introduce and study some general principles and hierarchical properties of expansions and restrictions of structures and their theories The general approach is applied to describe these properties for classes of $\omega$-categorical…
There is a long history of studying Ramsey theory using the algebraic structure of the Stone-\v{C}ech compactification of discrete semigroup. It has been shown that various Ramsey theoretic structures are contained in different algebraic…
In the course of classifying the homogeneous permutations, Cameron introduced the viewpoint of permutations as structures in a language of two linear orders, and this structural viewpoint is taken up here. The majority of this thesis is…
The uniqueness theorem for a two-parameter extended relative entropy is proven. This result extends our previous one, the uniqueness theorem for a one-parameter extended relative entropy, to a two-parameter case. In addition, the properties…
Let $\mathfrak{P}$ be a topological property. We study the relation between the order structure of the set of all $\mathfrak{P}$-extensions of a completely regular space $X$ with compact remainder (partially ordered by the standard partial…
In this short survey article, we try to list maximum number of known results on class preserving automorphisms of finite $p$-groups. We conclude the survey with some interesting (at least for the author) open problems on this topic.
This survey describes some recent work, by the authors and others, on the existence of algebraic fibrations of group extensions, as well as the finiteness properties of their algebraic fibers, in the realm of both abstract and pro-$p$…