7 citations · 15 across the 19 of their papers we have counts for
27 papers
Rokhlin properties in homeomorphism groups of compact metric spaces
Maciej Malicki
We develop a general framework for studying generic homeomorphisms of compact metric spaces using combinatorial amalgamation methods inspired by Fraïssé theory. Our approach combin…
Universal homogeneous two-sorted ultrametric spaces
Adam Bartoš, Wiesław Kubiś, Aleksandra Kwiatkowska +1
We view ultrametric spaces as two-sorted structures consisting of a set of points and of a linearly ordered set of distances. We call the appropriate notion of embeddings distance-…
Generic dc-automorphisms of two-sorted ultrametric spaces
Adam Bartoš, Wiesław Kubiś, Aleksandra Kwiatkowska +1
We continue to study ultrametric spaces as two-sorted structures consisting of a set of points and of a linearly ordered set of distances, together with the dc-embeddings, which we…
A logic of co-valuations
Maciej Malicki
A co-valuation is, essentially, a minimal finite cover. We introduce a logic based on co-valuations, which play the role of valuations of free variables in classical first-order lo…
Isomorphism of almost locally compact Polish metric structures
Maciej Malicki
A topological space is almost locally compact if it contains a dense locally compact subspace. We generalize a result from \cite{Ma}, showing that isomorphism on Borel classes of a…
Automorphism groups of measures on the Cantor space. Part I: Good measures and Rokhlin properties
Michal Doucha, Dominik Kwietniak, Maciej Malicki +1
We study criteria for the existence of a dense or comeager conjugacy class in the automorphism group of a given measure on the Cantor space. We concentrate on good measures, define…
The rational Gurarii space and its linear isometry group
Ondřej Kurka, Maciej Malicki
We show that the classes of partial isometries in finite-dimensional polyhedral spaces and in finite-dimensional rational polyhedral spaces do not have the weak amalgamation proper…
Homeomorphisms of the Pseudoarc
Tristan Bice, Maciej Malicki
We construct homeomorphisms of compacta from relations between finite graphs representing their open covers. Applied to the pseudoarc, this yields simple Fraïssé theoretic proofs o…
Isomorphism of locally compact Polish metric structures
Maciej Malicki
We study the isomorphism relation on Borel classes of locally compact Polish metric structures. We prove that isomorphism on such classes is always classifiable by countable struct…
Continuous logic and Borel equivalence relations
Andreas Hallbäck, Maciej Malicki, Todor Tsankov
We study the complexity of isomorphism of classes of metric structures using methods from infinitary continuous logic. For Borel classes of locally compact structures, we prove tha…
On Polish groups admitting non-essentially countable actions
Alexander S. Kechris, Maciej Malicki, Aristotelis Panagiotopoulos +1
It is a long-standing open question whether every Polish group that is not locally compact admits a Borel action on a standard Borel space whose associated orbit equivalence relati…
Remarks on weak amalgamation and large conjugacy classes in non-archimedean groups
Maciej Malicki
We study the notion of weak amalgamation in the context of diagonal conjugacy classes. Generalizing results of Kechris and Rosendal, we prove that for every countable structure …
Ordered structures and large conjugacy classes
Aleksandra Kwiatkowska, Maciej Malicki
This article is a contribution to the following problem: does there exist a Polish non-archimedean group (equivalently: automorphism group of a Fraisse limit) that is extremely ame…
Topologically 2-generated groups
Aleksandra Kwiatkowska, Maciej Malicki
We prove that for a number of ultrahomogeneous structures , including those with the free amalgamation property, the powers of the automorphism group , $n=1,2,\…
Property (T), finite-dimensional representations, and generic representations
Michal Doucha, Maciej Malicki, Alain Valette
Let be a discrete group with property (T). It is a standard fact that, in a unitary representation of on a Hilbert space , almost invariant vectors are close t…
Generic representations of countable groups
Michal Doucha, Maciej Malicki
The paper is devoted to a study of generic representations (homomorphisms) of discrete countable groups in Polish groups , i.e. those elements in the Polish space $\mathrm{R…
Automorphism groups of countable structures and groups of measurable functions
Aleksandra Kwiatkowska, Maciej Malicki
Let be a topological group and let be the Lebesgue measure on the interval . We let to be the topological group of all -equivalence classes of -measur…
An example of a non non-archimedean Polish group with ample generics
Maciej Malicki
For an analytic -ideal , is the Polish group of all the permutations of whose support is in , with Polish topology given by the corresponding submeasure…
Matheme and mathematics. On the main concepts of the philosophy of Alain Badiou
Maciej Malicki
In this paper, I present a critical discussion of mathematical arguments employed in the philosophy of event of Alain Badiou. On the basis of "Being and Event" as well as his other…
Abelian pro-countable groups and non-Borel orbit equivalence relations
Maciej Malicki
We study topological groups that can be defined as Polish, pro-countable abelian groups, as non-archimedean abelian groups or as quasi-countable abelian groups, i.e., Polish subdir…
Consequences of the existence of ample generics and automorphism groups of homogeneous metric structures
Maciej Malicki
We define a simple criterion for a homogeneous, complete metric structure that implies that the automorphism group $\mbox{Aut}(X)$ satisfies all the main consequences of the ex…
Abelian pro-countable groups and orbit equivalence relations
Maciej Malicki
We study groups that can be defined as Polish, pro-countable groups, as non-archimedean groups with an invariant metric or as quasi-countable groups, i.e., closed subdirect product…
Generic elements in isometry groups of Polish ultrametric spaces
Maciej Malicki
This paper presents a study of generic elements in full isometry groups of Polish ultrametric spaces. We obtain a complete characterization of Polish ultrametric spaces X whose iso…
Cooperative Boolean systems with generically long attractors II
Winfried Just, Maciej Malicki
We prove that cooperativity in Boolean networks precludes a strong notion of sensitive dependence on initial conditions. Weaker notions of sensitive dependence are shown to be cons…