Admissible extensions of subtheories of second order arithmetic

2022/02/07 by Jäger, Gerhard, Rathjen, Michael
#03B15 #03C70 #03E30 #03F05 #03F15 #03F25 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2202.03476

Abstract

In this paper we study admissible extensions of several theories T of reverse mathematics. The idea is that in such an extension the structure M = (N,S,∈) of the natural numbers N and collection of sets of natural numbers S has to obey the axioms of T while simultaneously one also has a set-theoretic world with transfinite levels erected on top of M governed by the axioms of Kripke-Platek set theory, KP.

Related

• Subsystems of Second Order Arithmetic
• Comparison of constructive multi-typed theory with subsystems of second order arithmetic
• End extending models of set theory via power admissible covers
• Reduced Set Theory
• Interpreting set theory in higher order arithmetic