Book ChapterDOI
Error and Predicativity
Laura Crosilla
- pp 13-22
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TLDR
The suggestion is that ideas originating in the predicativity debate as a reply to foundational errors are now having profound influence to the way the authors try to address the issue of local errors.Abstract:
The article surveys ideas emerging within the predicative tradition in the foundations of mathematics, and attempts a reading of predicativity constraints as highlighting different levels of understanding in mathematics. A connection is made with two kinds of error which appear in mathematics: local and foundational errors. The suggestion is that ideas originating in the predicativity debate as a reply to foundational errors are now having profound influence to the way we try to address the issue of local errors. Here fundamental new interactions between computer science and mathematics emerge.read more
Citations
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Bounded Arithmetic と計算量の根本問題
TL;DR: Theorem 10: (Cut Elimination Theorem for Second Order Logic 171 as mentioned in this paper is a cut elimination theorem for first-order logic that guarantees that C R inferences are still valid after the substitution of V for a.
Journal Article
Review: Wilfried Buchholz, Wolfram Pohlers, Wilfried Sieg, Iterated Inductive Definitions and Subsystems of Analysis
Journal Article
Review: G. Kreisel, Ordinal Logics and the Characterization of Informal Concepts of Proof
Book ChapterDOI
Predicativity and Feferman
TL;DR: Predicativity has been at the center of a considerable part of Feferman's work and has been explored alternative ways of explicating and analyzing this notion and has shown that predicative mathematics extends much further than expected within ordinary mathematics.
References
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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.
Journal ArticleDOI
Logic, Methodology and Philosophy of Science
Book ChapterDOI
An Intuitionistic Theory of Types: Predicative Part
TL;DR: The theory of types as mentioned in this paper is a full-scale system for formalizing intuitionistic mathematics as developed, which allows proofs to appear as parts of propositions so that the propositions of the theory can express properties of proofs.
Book ChapterDOI
Constructive mathematics and computer programming
TL;DR: This chapter discusses that relating constructive mathematics to computer programming seems to be beneficial, and that it may well be possible to turn what is now regarded as a high level programming language into machine code by the invention of new hardware.
Journal ArticleDOI