2019/03/14 by Ayana Hirata, Hajime Ishihara, Hirata, Ayana +5
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Logic, Reasoning, and Knowledge #math.LO #msc:03E70 #msc:03F50 #msc:06D22 #msc:54A05
paper · pdf · doi:10.48550/arxiv.1903.05852
Corrected some typographical errors
arxiv created 2019/06/22 · arxiv updated 2019/06/25
We present statements equivalent to some fragments of the principle of non-deterministic inductive definitions (NID) by van den Berg (2013), working in a weak subsystem of constructive set theory CZF. We show that several statements in constructive topology which were initially proved using NID are equivalent to the elementary and finitary NIDs. We also show that the finitary NID is equivalent to its binary fragment and that the elementary NID is equivalent to a variant of NID based on the notion of biclosed subset. Our result suggests that proving these statements in constructive topology requires genuine extensions of CZF with the elementary or finitary NID.