Zobrazeno 1 - 10
of 62
pro vyhledávání: '"Panagiotopoulos, Aristotelis"'
Countable $\mathcal{L}$-structures $\mathcal{N}$ whose isomorphism class supports a permutation invariant probability measure in the logic action have been characterized by Ackerman-Freer-Patel to be precisely those $\mathcal{N}$ which have no algebr
Externí odkaz:
http://arxiv.org/abs/2408.07454
For each ordinal $\alpha<\omega_1$, we introduce the class of $\alpha$-balanced Polish groups. These classes form a hierarchy that completely stratifies the space between the class of Polish groups admitting a two-side-invariant metric (TSI) and the
Externí odkaz:
http://arxiv.org/abs/2406.06082
We show that the homeomorphisms of the Sierpi\'nski carpet are not classifiable, up to conjugacy, using isomorphism types of countable structures as invariants.
Comment: 13 pages, 6 figures
Comment: 13 pages, 6 figures
Externí odkaz:
http://arxiv.org/abs/2404.01472
Publikováno v:
Physical Review Letters, Vol. 131, No. 17, p. 171402 (23 October, 2023)
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 rich enough collections of spacetimes is Borel definable. In fact, we
Externí odkaz:
http://arxiv.org/abs/2305.04818
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 algebraic topology. In it, we show that the \v{C}ech cohomology functors $\c
Externí odkaz:
http://arxiv.org/abs/2210.11098
Let $E$ be a countable Borel equivalence relation on the space $\mathcal{E}_{\infty}$ of all infinite partitions of the natural numbers. We show that $E$ coincides with equality below a Carlson-Simpson generic element of $\mathcal{E}_{\infty}$. In co
Externí odkaz:
http://arxiv.org/abs/2206.14224
Publikováno v:
In Annals of Pure and Applied Logic May 2024 175(5)
The algebraic dimension of a Polish permutation group $Q\leq \mathrm{Sym}(\mathbb{N})$ is the smallest $n\in\omega$, so that for all $A\subseteq \mathbb{N}$ of size $n+1$, the orbit of every $a\in A$ under the pointwise stabilizer of $A\setminus\{a\}
Externí odkaz:
http://arxiv.org/abs/2105.04989
We show that the existence of a universal structure implies the existence of a generic structure for any approximable class $\mathcal{C}$ of countable structures. We also show that the converse is not true. As a consequence, we provide several new ex
Externí odkaz:
http://arxiv.org/abs/2104.13222
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 the moment there is a gap in the proof of Theorem 2.
Comment: Work
Comment: Work
Externí odkaz:
http://arxiv.org/abs/2012.04376