Non-deterministic inductive definitions

2011/04/14 by Benno van den Berg, Berg, Benno van den
Mathematics · Psychology · #03E70 #06D22 #18B30 #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Philosophy and Theoretical Science #math.LO #msc:03E70 #msc:06D22 #msc:18B30

paper · pdf · doi:10.48550/arxiv.1104.2744

openalex publication_date 2011/04/14 · arxiv created 2012/09/14 · arxiv updated 2012/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a new proof principle in the context of constructive Zermelo-Fraenkel set theory based on what we will call "non-deterministic inductive definitions". We give applications to formal topology as well as a predicative justification of this principle.

Related

• Equivalents of the finitary non-deterministic inductive definitions
• Proof Theory of Constructive Systems: Inductive Types and Univalence
• Constructive Zermelo-Fraenkel set theory and the limited principle of omniscience
• Independence Phenomena in Mathematics: a Set Theoretic Perspective on Current Obstacles and Scenarios for Solutions
• Finite enumerable but undecidable collections