Zobrazeno 1 - 10
of 235
pro vyhledávání: '"SLAMAN, THEODORE A."'
We show that if $E$ is a countable Borel equivalence relation on $\mathbb{R}^n$, then there is a closed subset $A \subset [0,1]^n$ of Hausdorff dimension $n$ so that $E \restriction A$ is smooth. More generally, if $\leq_Q$ is a locally countable Bor
Externí odkaz:
http://arxiv.org/abs/2410.22034
We investigate natural variations of behaviourally correct learning and explanatory learning -- two learning paradigms studied in algorithmic learning theory -- that allow us to ``learn'' equivalence relations on Polish spaces. We give a characteriza
Externí odkaz:
http://arxiv.org/abs/2403.17493
Autor:
Lerman, Manuel, Slaman, Theodore A.
Publikováno v:
The Bulletin of Symbolic Logic, 2022 Mar 01. 28(1), 150-155.
Externí odkaz:
https://www.jstor.org/stable/27115426
Autor:
Reimann, Jan, Slaman, Theodore A.
We investigate which infinite binary sequences (reals) are effectively random with respect to some continuous (i.e., non-atomic) probability measure. We prove that for every n, all but countably many reals are n-random for such a measure, where n ind
Externí odkaz:
http://arxiv.org/abs/1808.10102
Autor:
Slaman, Theodore A., Yokoyama, Keita
In this paper, we show that $\mathrm{RT}^{2}+\mathsf{WKL}_0$ is a $\Pi^{1}_{1}$-conservative extension of $\mathrm{B}\Sigma^0_3$.
Comment: 9 pages
Comment: 9 pages
Externí odkaz:
http://arxiv.org/abs/1711.08704
We give a construction of an absolutely normal real number $x$ such that for every integer $b $ greater than or equal to $2$, the discrepancy of the first $N$ terms of the sequence $(b^n x \mod 1)_{n\geq 0}$ is of asymptotic order $\mathcal{O}(N^{-1/
Externí odkaz:
http://arxiv.org/abs/1707.02628
We construct the base $2$ expansion of an absolutely normal real number $x$ so that, for every integer $b$ greater than or equal to $2$, the discrepancy modulo $1$ of the sequence $(b^0 x, b^1 x, b^2 x , \ldots)$ is essentially the same as that reali
Externí odkaz:
http://arxiv.org/abs/1702.04072
We show that there is a strong minimal pair in the computably enumerable Turing degrees.
Externí odkaz:
http://arxiv.org/abs/1610.03591
We generalize the classical theorem by Jarnik and Besicovitch on the irrationality exponents of real numbers and Hausdorff dimension. Let a be any real number greater than or equal to 2 and let b be any non-negative real less than or equal to 2/a. We
Externí odkaz:
http://arxiv.org/abs/1601.00153
Publikováno v:
In Advances in Mathematics 4 June 2021 383