Interpreting set theory in higher order arithmetic
Colin McLarty
TL;DR
This paper formalizes the relationship between higher order arithmetic and set theory with limited power set, clarifying the proof-theoretic strength of these systems.
Contribution
It precisely characterizes the proof-theoretic strength of higher order arithmetic in terms of various ZF-based axiom systems.
Findings
Higher order arithmetic aligns with set theory with limited power set.
The paper provides formal equivalences between these systems.
Clarifies the proof-theoretic boundaries of higher order arithmetic.
Abstract
A folk theorem says higher order arithmetic has the proof theoretic strength of set theory with limited power set. This paper makes the theorem precise in terms of several axiom system based on ZF.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Mathematical and Theoretical Analysis · Numerical Methods and Algorithms