On Use of an Explicit Congruence Predicate in Bounded Arithmetic
Logic
2009-04-03 v1
Abstract
We introduce system S^2_0E, a bounded arithmetic corresponding to Buss's S^2_0 with the predicate E which signifies the existence of the value. Then, we show that we can \Sigma^b_2-define truthness of S^2_0 E and therefore we can prove consistency of S^2_0 E in S^2_2. Finally, we conjecture that S^2_0 E + \Sigma^b_1-PIND interprets S^2_1.
Cite
@article{arxiv.0904.0335,
title = {On Use of an Explicit Congruence Predicate in Bounded Arithmetic},
author = {Yoriyuki Yamagata},
journal= {arXiv preprint arXiv:0904.0335},
year = {2009}
}
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17 Pages