Hierarchies of Subsystems of Weak Arithmetic
Shahram Mohsenipour
TL;DR
This paper provides a complete characterization of the logical hierarchy among various subsystems of weak arithmetic, clarifying their relationships and differences.
Contribution
It offers a comprehensive analysis of the logical structure of multiple weak arithmetic subsystems, which was previously not fully understood.
Findings
Complete logical hierarchy of weak arithmetic subsystems established
Differences between subsystems like ZR, OI, and their extensions clarified
Framework for comparing weak arithmetic systems developed
Abstract
We completely characterize the logical hierarchy of various subsystems of weak arithmetic, namely: ZR, ZR + N, ZR + GCD, ZR + Bez, OI + N, OI + GCD, OI + Bez.
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