Zobrazeno 1 - 10
of 537
pro vyhledávání: '"03B30"'
Autor:
Neri, Morenikeji
We explore the computational content of Kronecker's lemma via the proof-theoretic perspective of proof mining and utilise the resulting finitary variant of this fundamental result to provide new rates for the Strong Law of Large Numbers for random va
Externí odkaz:
http://arxiv.org/abs/2411.08620
Autor:
Freund, Anton, Uftring, Patrick
We prove conservativity results for weak K\H{o}nig's lemma that extend the celebrated result of Harrington (for $\Pi^1_1$-statements) and are somewhat orthogonal to the extension by Simpson, Tanaka and Yamazaki (for statements of the form $\forall X\
Externí odkaz:
http://arxiv.org/abs/2410.20591
Autor:
Marcone, Alberto, Osso, Gian Marco
This paper classifies different fragments of the Galvin-Prikry theorem, an infinite dimensional generalization of Ramsey's theorem, in terms of their uniform computational content (Weihrauch degree). It can be seen as a continuation of arXiv:2003.042
Externí odkaz:
http://arxiv.org/abs/2410.06928
Autor:
Li, Ang
This paper continues to study the connection between reverse mathematics and Weihrauch reducibility. In particular, we study the problems formed from Maltsev's theorem on the order types of countable ordered groups. Solomon showed that the theorem is
Externí odkaz:
http://arxiv.org/abs/2409.19229
Autor:
Sanders, Sam
A central topic in mathematical logic is the classification of theorems from mathematics in hierarchies according to their logical strength. Ideally, the place of a theorem in a hierarchy does not depend on the representation (aka coding) used. In th
Externí odkaz:
http://arxiv.org/abs/2409.04562
Autor:
Sanders, Sam
Going back to Kreisel in the Sixties, hyperarithmetical analysis is a cluster of logical systems just beyond arithmetical comprehension. Only recently natural examples of theorems from the mathematical mainstream were identified that fit this categor
Externí odkaz:
http://arxiv.org/abs/2408.13760
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
The infinite pigeonhole principle for $k$ colors ($\mathsf{RT}_k$) states, for every $k$-partition $A_0 \sqcup \dots \sqcup A_{k-1} = \mathbb{N}$, the existence of an infinite subset~$H \subseteq A_i$ for some~$i < k$. This seemingly trivial combinat
Externí odkaz:
http://arxiv.org/abs/2407.01236
Autor:
Freund, Anton
Fra\"iss\'e's conjecture (proved by Laver) is implied by the $\Pi^1_1$-comprehension axiom of reverse mathematics, as shown by Montalb\'an. The implication must be strict for reasons of quantifier complexity, but it seems that no better bound has bee
Externí odkaz:
http://arxiv.org/abs/2406.13485
Autor:
Normann, Dag, Sanders, Sam
The program Reverse Mathematics in the foundations of mathematics seeks to identify the minimal axioms required to prove theorems of ordinary mathematics. One always assumes the base theory, a logical system embodying computable mathematics. As it tu
Externí odkaz:
http://arxiv.org/abs/2406.10716