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pro vyhledávání: '"Andretta, Alessandro"'
Autor:
Andretta, Alessandro, Notaro, Lorenzo
Generalizing a result of T\"ornquist and Weiss, we study the connection between the existence of $\varSigma_2^1$ Sierpi\'{n}ski's coverings of $\mathbb{R}^n$, and a cardinal invariant of the upper semi-lattice of constructibility degrees known as bre
Externí odkaz:
http://arxiv.org/abs/2408.10182
Autor:
Andretta, Alessandro, Izmestiev, Ivan
For all $d \geq 3$ we show that the cardinality of $ \mathbb{R} $ is at most $\aleph_n $ if and only if $ \mathbb{R}^d $ can be covered with $ ( n + 1 ) ( d - 1 ) + 1 $ sprays whose centers are in general position in a hyperplane. This extends previo
Externí odkaz:
http://arxiv.org/abs/2406.04078
Autor:
Andretta, Alessandro, Notaro, Lorenzo
The Axiom of Dependent Choice $\mathsf{DC}$ and the Axiom of Countable Choice $\mathsf{AC}_\omega$ are two weak forms of the Axiom of Choice that can be stated for a specific set: $\mathsf{DC}(X)$ asserts that any total binary relation on $X$ has an
Externí odkaz:
http://arxiv.org/abs/2305.06676
In this paper we introduce a new hierarchy of large cardinals between I3 and I2, the iterability hierarchy, and we prove that every step of it strongly implies the ones below.
Comment: Archive for Mathematical Logic (2018)
Comment: Archive for Mathematical Logic (2018)
Externí odkaz:
http://arxiv.org/abs/1712.03877
We study the density function of measurable subsets of the Cantor space. Among other things, we identify a universal set $\mathcal{U}$ for $\Sigma^{1}_{1}$ subsets of $( 0 ; 1 )$ in terms of the density function; specifically $\mathcal{U}$ is the set
Externí odkaz:
http://arxiv.org/abs/1705.02285
Akademický článek
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Autor:
Andretta, Alessandro, Ros, Luca Motto
We provide analogues of the results from [FMR11, CMMR13] in the reference list (which correspond to the case $\kappa = \omega$) for arbitrary $\kappa$-Souslin quasi-orders on any Polish space, for $\kappa$ an infinite cardinal smaller than the cardin
Externí odkaz:
http://arxiv.org/abs/1609.09292
Work in the measure algebra of the Lebesgue measure on the Cantor space: for comeager many $[A]$ the set of points $x$ such that the density of $x $ at $A$ is not defined is $\Sigma^{0}_{3}$-complete; for some compact $K$ the set of points $x$ such t
Externí odkaz:
http://arxiv.org/abs/1510.04193
Given an equivalence class $[A]$ in the measure algebra of the Cantor space, let $\hat\Phi([A])$ be the set of points having density 1 in $A$. Sets of the form $\hat\Phi([A])$ are called $\mathcal{T}$-regular. We establish several results about $\mat
Externí odkaz:
http://arxiv.org/abs/1105.3355