Introduction to clarithmetic II
Logic in Computer Science
2016-06-24 v6 Computational Complexity
Logic
Number Theory
Abstract
The earlier paper "Introduction to clarithmetic I" constructed an axiomatic system of arithmetic based on computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html), and proved its soundness and extensional completeness with respect to polynomial time computability. The present paper elaborates three additional sound and complete systems in the same style and sense: one for polynomial space computability, one for elementary recursive time (and/or space) computability, and one for primitive recursive time (and/or space) computability.
Cite
@article{arxiv.1004.3236,
title = {Introduction to clarithmetic II},
author = {Giorgi Japaridze},
journal= {arXiv preprint arXiv:1004.3236},
year = {2016}
}