Note on $\Pi^0_{n+1}$-LEM, $\Sigma^0_{n+1}$-LEM and $\Sigma^0_{n+1}$-DNE
Logic
2018-07-30 v1
Abstract
We show that results of Akama, Berardi, Hayashi and Kohlenbach, on the relative independence of certain arithmetical principles over intuitionistic arithmetic HA, hold also over Kleene and Vesley's system FIM of intuitionistic analysis, which extends HA and is consistent with classical arithmetic but not with classical analysis. The double negations of the universal closures of these principles are also considered, and shown to behave differently with respect to HA and FIM. Various elementary questions are left open.
Keywords
Cite
@article{arxiv.1807.10472,
title = {Note on $\Pi^0_{n+1}$-LEM, $\Sigma^0_{n+1}$-LEM and $\Sigma^0_{n+1}$-DNE},
author = {Joan R. Moschovakis},
journal= {arXiv preprint arXiv:1807.10472},
year = {2018}
}
Comments
Extended abstract of contributed talk, 5th Panhellenic Logic Symposium, July 25-28, 2005 in Athens, Greece