Intuitionistic notions of boundedness in ℕ

✍ Scribed by Fred Richman

• Publisher: John Wiley and Sons
• Year: 2009
• Tongue: English
• Weight: 97 KB
• Volume: 55
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.200710072

✦ Synopsis

Abstract

We consider notions of boundedness of subsets of the natural numbers ℕ that occur when doing mathematics in the context of intuitionistic logic. We obtain a new characterization of the notion of a pseudobounded subset and we formulate the closely related notion of a detachably finite subset. We establish metric equivalents for a subset of ℕ to be detachably finite and to satisfy the ascending chain condition. Following Ishihara, we spell out the relationship between detachable finiteness and sequential continuity. Most of the results do not require countable choice. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)