Zobrazeno 1 - 10
of 95
pro vyhledávání: '"Hoelzl, Rupert"'
The well-known $abc$-conjecture concerns triples $(a,b,c)$ of non-zero integers that are coprime and satisfy ${a+b+c=0}$. The strong $n$-conjecture is a generalisation to $n$ summands where integer solutions of the equation ${a_1 + \ldots + a_n = 0}$
Externí odkaz:
http://arxiv.org/abs/2409.13439
We continue the project of the study of reverse mathematics principles inspired by cardinal invariants. In this article in particular we focus on principles encapsulating the existence of large families of objects that are in some sense mutually inde
Externí odkaz:
http://arxiv.org/abs/2408.09796
Autor:
Hölzl, Rupert, Ng, Keng Meng
The Weihrauch degrees are a tool to gauge the computational difficulty of mathematical problems. Often, what makes these problems hard is their discontinuity. We look at discontinuity in its purest form, that is, at otherwise constant functions that
Externí odkaz:
http://arxiv.org/abs/2405.04338
Speedable numbers are real numbers which are algorithmically approximable from below and whose approximations can be accelerated nonuniformly. We begin this article by answering a question of Barmpalias by separating a strict subclass that we will re
Externí odkaz:
http://arxiv.org/abs/2404.15811
Autor:
Hölzl, Rupert, Janicki, Philip
A left-computable number $x$ is called regainingly approximable if there is a computable increasing sequence $(x_n)_n$ of rational numbers converging to $x$ such that $x - x_n < 2^{-n}$ for infinitely many $n \in \mathbb{N}$; and it is called nearly
Externí odkaz:
http://arxiv.org/abs/2303.11986
We call an $\alpha \in \mathbb{R}$ regainingly approximable if there exists a computable nondecreasing sequence $(a_n)_n$ of rational numbers converging to $\alpha$ with $\alpha - a_n < 2^{-n}$ for infinitely many $n \in \mathbb{N}$. We also call a s
Externí odkaz:
http://arxiv.org/abs/2301.03285
We develop a systematic algorithmic framework that unites global and local classification problems using index sets. We prove that the classification problem for continuous (binary) regular functions among almost everywhere linear, pointwise linear-t
Externí odkaz:
http://arxiv.org/abs/2010.09499
Autor:
Hölzl, Rupert, Porter, Christopher P.
In this survey we discuss work of Levin and V'yugin on collections of sequences that are non-negligible in the sense that they can be computed by a probabilistic algorithm with positive probability. More precisely, Levin and V'yugin introduced an ord
Externí odkaz:
http://arxiv.org/abs/1907.07815
Autor:
HÖLZL, RUPERT, PORTER, CHRISTOPHER P.
Publikováno v:
The Bulletin of Symbolic Logic, 2022 Mar 01. 28(1), 27-70.
Externí odkaz:
https://www.jstor.org/stable/27115422
Autor:
Hölzl, Rupert, Porter, Christopher P.
Publikováno v:
J. symb. log. 84 (2019) 1527-1543
We show that for each computable ordinal $\alpha>0$ it is possible to find in each Martin-L\"of random $\Delta^0_2$ degree a sequence $R$ of Cantor-Bendixson rank $\alpha$, while ensuring that the sequences that inductively witness $R$'s rank are all
Externí odkaz:
http://arxiv.org/abs/1707.00378