7 citations · 18 across the 18 of their papers we have counts for
20 papers
Quasi-invariant measures concentrating on countable structures
Clinton Conley, Colin Jahel, Aristotelis Panagiotopoulos
Countable -structures whose isomorphism class supports a permutation invariant probability measure in the logic action have been characterized by Ackerma…
The class and dynamics of -balanced Polish groups
Shaun Allison, Aristotelis Panagiotopoulos
For each ordinal , we introduce the class of -balanced Polish groups. These classes form a hierarchy that completely stratifies the space between the class of Polish grou…
The homeomorphisms of the Sierpiński carpet are not classifiable by countable structures
Dhruv Kulshreshtha, Aristotelis Panagiotopoulos
We show that the homeomorphisms of the Sierpiński carpet are not classifiable, up to conjugacy, using isomorphism types of countable structures as invariants.
Incompleteness Theorems for Observables in General Relativity
Aristotelis Panagiotopoulos, George Sparling, Marios Christodoulou
The quest for complete observables in general relativity has been a longstanding open problem. We employ methods from descriptive set theory to show that no complete observable on…
The definable content of homological invariants II: Čech cohomology and homotopy classification
Jeffrey Bergfalk, Martino Lupini, Aristotelis Panagiotopoulos
This is the second installment in a series of papers applying descriptive set theoretic techniques to both analyze and enrich classical functors from homological algebra and algebr…
Every CBER is smooth below the Carlson-Simpson generic partition
Aristotelis Panagiotopoulos, Allison Wang
Let be a countable Borel equivalence relation on the space of all infinite partitions of the natural numbers. We show that coincides with equality be…
Strong ergodicity phenomena for Bernoulli shifts of bounded algebraic dimension
Aristotelis Panagiotopoulos, Assaf Shani
The algebraic dimension of a Polish permutation group is the smallest , so that for all of size , the orbit of…
Universality vs Genericity and -free graphs
Aristotelis Panagiotopoulos, Katrin Tent
We show that the existence of a universal structure implies the existence of a generic structure for any approximable class of countable structures. We also show that…
The automorphism group of the random poset does not admit a generic pair
Aleksandra Kwiatkowska, Aristotelis Panagiotopoulos
We show that the conjugacy class of every pair of automoprhisms of the random poset is meager. This answers a question of Truss; see also Kuske-Truss. EDIT. Work in progress, at th…
The definable content of homological invariants I: &
Jeffrey Bergfalk, Martino Lupini, Aristotelis Panagiotopoulos
This is the first installment in a series of papers in which we illustrate how classical invariants of homological algebra and algebraic topology can be enriched with additional de…
Dynamical obstructions to classification by (co)homology and other TSI-group invariants
Shaun Allison, Aristotelis Panagiotopoulos
In the spirit of Hjorth's turbulence theory, we introduce "unbalancedness": a new dynamical obstruction to classifying orbit equivalence relations by actions of Polish groups which…
The generic combinatorial simplex
Aristotelis Panagiotopoulos, Sławomir Solecki
We employ projective Fraïssé theory to define the "generic combinatorial -simplex" as the pro-finite, simplicial complex that is canonically associated with a family of simply d…
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…
Definable (co)homology, pro-torus rigidity, and (co)homological classification
Jeffrey Bergfalk, Martino Lupini, Aristotelis Panagiotopoulos
We show that the classical homology theory of Steenrod may be enriched with descriptive set-theoretic information. We prove that the resulting definable homology theory provides a…
Examples of weak amalgamation classes
Adam Krawczyk, Alex Kruckman, Wiesław Kubiś +1
We present several examples of hereditary classes of finite structures satisfying the joint embedding property and the weak amalgamation property, but failing the cofinal amalgamat…
Higher dimensional obstructions for star reductions
Alex Kruckman, Aristotelis Panagiotopoulos
A -reduction between two equivalence relations is a Baire measurable reduction which preserves generic notions, i.e., preimages of meager sets are meager. We show that a -red…
A combinatorial model for the Menger curve
Aristotelis Panagiotopoulos, Slawomir Solecki
We represent the universal Menger curve as the topological realization of the projective Fraïssé limit of the class of all finite connected graphs. We…
Games orbits play and obstructions to Borel reducibility
Martino Lupini, Aristotelis Panagiotopoulos
We introduce a new, game-theoretic approach to anti-classification results for orbit equivalence relations. Within this framework, we give a short conceptual proof of Hjorth's turb…
Compact spaces as quotients of projective Fraisse limits
Aristotelis Panagiotopoulos
We develop a theory of projective Fraisse limits in the spirit of Irwin- Solecki. The structures here will additionally support dual semantics as in [Sl10, Sl12]. Let Y be a compac…
Extentability of Automorphisms of Generic Substructures
Aristotelis Panagiotopoulos
We show that if g is a generic (in the sense of Baire category) isometry of a generic subspace of the Urysohn metric space U, then g does not extend to a full isometry of U. The sa…