Book ChapterDOI
Intuitionistic Provability versus Uniform Provability in \mathsf{RCA}
Makoto Fujiwara
- pp 186-195
Reads0
Chats0
TLDR
It is shown that for any \(\Pi _{2}^{1}\) sentence of some syntactical form, it is intuitionistically provable if and only if it is uniformly provable in \(\mathsf {RCA}\).Abstract:
We provide an exact formalization of uniform provability in \(\mathsf {RCA}\) and show that for any \(\Pi _{2}^{1}\) sentence of some syntactical form, it is intuitionistically provable if and only if it is uniformly provable in \(\mathsf {RCA}\).read more
Citations
More filters
Journal ArticleDOI
Interrelation between weak fragments of double negation shift and related principles
TL;DR: Two weak fragments of the double negation shift schema are investigated, motivated, respectively, from Spector’s consistency proof of ACA0 and from the negative translation of RCA0, as well as double negated variants of logical principles.
Journal ArticleDOI
On weihrauch reducibility and intuitionistic reverse mathematics
TL;DR: The authors showed that Weihrauch reducibility to the composition of finitely many instances of a theorem is captured by provability in EL0 together with Markov's principle.
Journal ArticleDOI
Weihrauch and constructive reducibility between existence statements
TL;DR: A meta-theorem is shown that the primitive recursive variants of Weihrauch reduction between existence statements in finite-type arithmetic is identical to some formal reducibility in the corresponding (nearly) intuitionistic finite- type arithmetic for all existence statements formalized with existential free formulas.
Posted Content
On Weihrauch Reducibility and Intuitionistic Reverse Mathematics
TL;DR: This article showed that Weihrauch reducibility to the composition of finitely many instances of a theorem is captured by provability in EL_0 together with Markov's principle.
References
More filters
Book
Computable Analysis : An Introduction
TL;DR: This book provides a solid fundament for studying various aspects of computability and complexity in analysis and is written in a style suitable for graduate-level and senior students in computer science and mathematics.
Book
Subsystems of Second Order Arithmetic
TL;DR: In this paper, the development of Mathematics within Subsystems of Z2 is discussed, with a focus on recursive comprehension and weak Konig's lemma, and a discussion of models of sub-systems.
Book ChapterDOI
Multi-index Mittag-Leffler Functions
TL;DR: In this paper, Dzherbashian [Dzh60] defined a function with positive α 1 > 0, α 2 > 0 and real α 1, β 2, β 3, β 4, β 5, β 6, β 7, β 8, β 9, β 10, β 11, β 12, β 13, β 14, β 15, β 16, β 17, β 18, β 20, β 21, β 22, β 24
BookDOI
Metamathematical investigation of intuitionistic arithmetic and analysis
TL;DR: In this paper, Kripke models are used to define inductive definitions, trees and ordinals for intuitionistic formal systems, and normalization theorems for systems of natural deduction.
Book
Applied Proof Theory: Proof Interpretations and their Use in Mathematics
TL;DR: This paper discusses the unwinding of proofs in approximation theory, semi-intuitionistic systems and monotone modified realizability, and the Friedman-Dragalin A-translation.