Zobrazeno 1 - 10
of 49
pro vyhledávání: '"03E15 03E60"'
Autor:
Medini, Andrea
All spaces are assumed to be separable and metrizable. We give a complete classification of the homogeneous zero-dimensional spaces, under the Axiom of Determinacy. This classification is expressed in terms of topological complexity (in the sense of
Externí odkaz:
http://arxiv.org/abs/2312.10735
Autor:
Levinson, Derek
We find bounds for the maximal length of a sequence of distinct $\bf{\Gamma_{2n+1,m}}$-sets under $AD$ and show there is no sequence of distinct $\bf{\Gamma_{2n+1}}$-sets of length $\bf{\delta^1_{2n+3}}$. As a special case, there is no sequence of di
Externí odkaz:
http://arxiv.org/abs/2312.00278
Autor:
Lutz, Patrick
The Solecki dichotomy in descriptive set theory and the Posner-Robinson theorem in computability theory bear a superficial resemblance to each other and can sometimes be used to prove the same results, but do not have any obvious direct relationship.
Externí odkaz:
http://arxiv.org/abs/2301.07259
Autor:
Yu, Liang
We prove that, assuming $\mathrm{ZF}$, and restricted to any pointed set, Chaitin's $\Omega_U:x\mapsto \Omega_U^x=\sum_{U^x(\sigma)\downarrow}2^{-|\sigma|}$ is not injective for any universal prefix-free Turing machine $U$, and that $\Omega_U^x$ fail
Externí odkaz:
http://arxiv.org/abs/2203.07576
Autor:
Medini, Andrea, Vidnyánszky, Zoltán
All spaces are assumed to be separable and metrizable. Ostrovsky showed that every zero-dimensional Borel space is $\sigma$-homogeneous. Inspired by this theorem, we obtain the following results: assuming $\mathsf{AD}$, every zero-dimensional space i
Externí odkaz:
http://arxiv.org/abs/2107.07747
We prove a local version of Gowers' Ramsey-type theorem [Ann. Math. 156 (2002)], as well as local versions both of the Banach space first dichotomy (the "unconditional/HI" dichotomy) of Gowers [Ann. Math. 156 (2002)] and of the third dichotomy (the "
Externí odkaz:
http://arxiv.org/abs/2005.06458
The Hausdorff $\delta$-dimension game was introduced by Das, Fishman, Simmons and {Urba{\'n}ski} and shown to characterize sets in $\mathbb{R}^d$ having Hausdorff dimension $\leq \delta$. We introduce a variation of this game which also characterizes
Externí odkaz:
http://arxiv.org/abs/2003.11578
Autor:
Schrittesser, David, Törnquist, Asger
We prove that under a principle of Ramsey regularity there are no infinite maximal almost disjoint families with respect to the transfinitely iterated Fr\'echet ideals. The results of the present paper were announced by the authors in the Proceedings
Externí odkaz:
http://arxiv.org/abs/2003.10944
We introduce the notion of $(\Gamma,E)$-determinacy for $\Gamma$ a pointclass and $E$ an equivalence relation on a Polish space $X$. A case of particular interest is the case when $E=E_G$ is the (left) shift-action of $G$ on $S^G$ where $S=2=\{0,1\}$
Externí odkaz:
http://arxiv.org/abs/2003.02238
Autor:
Saveliev, Denis I.
We show that for every Tychonoff space $X$ and Hausdorff operation $\mathbf\Phi$, the class $\mathbf\Phi(\mathscr Z,X)$ generated from zero sets in $X$ by $\mathbf\Phi$ has the reduction or separation property if the corresponding class $\mathbf\Phi(
Externí odkaz:
http://arxiv.org/abs/2001.02033