Work

Notes on the Equiconsistency of ZFC Without the Power Set Axiom and Second-Order Arithmetic

Year: 2025

Type: article

Abstract: We demonstrate that theories Z−, ZF−, ZFC− (minus means the absence of the Power Set axiom) and PA2, PA2− (minus means the absence of the Countable Choice schema) are equiconsistent to each other. The methods used include the interpretation of a power-less set theory in PA2− via well-founded trees, as well as the Gödel constructibility in said power-less set theory.

Source: Axioms

DOI: 10.3390/axioms14120865

Authors: Vladimir Kanovei, Vassily Lyubetsky

Institutions: Russian Academy of Sciences, Institute for Information Transmission Problems

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: Ministry of Education and Science of the Russian Federation