Equivalents of the finitary non-deterministic inductive definitions
Logic
2019-06-25 v3
Abstract
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.
Keywords
Cite
@article{arxiv.1903.05852,
title = {Equivalents of the finitary non-deterministic inductive definitions},
author = {Ayana Hirata and Hajime Ishihara and Tatsuji Kawai and Takako Nemoto},
journal= {arXiv preprint arXiv:1903.05852},
year = {2019}
}
Comments
Corrected some typographical errors