Refinement is equivalent to Fullness

✍ Scribed by Albert Ziegler

• Book ID: 102487133
• Publisher: John Wiley and Sons
• Year: 2010
• Tongue: English
• Weight: 78 KB
• Volume: 56
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.200910115

✦ Synopsis

Abstract

In the article [4], a new constructive set theoretic principle called Refinement was introduced and analysed. While it seemed to be significantly weaker than its alternative, the more established axiom of Fullness (a constructive version of the Powerset axiom from classical set theory), it was shown to suffice to imply many of the mathematically important consequences. In this article, we will define for each set A a set of truth values which measures the complexity of the equality relation on A. Using these sets we will show that Refinement is actually equivalent to Fullness on the basis of the other axioms of constructive Zermelo‐Fraenkel set theory (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)