An equiconsistency proof for CZF + V = L
Abstract
In many axiomatic set theories, Gödel's constructible universe L is known as an inner model, that is, a definable class satisfying the same axioms (and containing the same ordinals). This gives a trivial proof that adding the axiom 𝑉 = 𝐿 does not increase the consistency strength of the theory. In this paper, we shall look at a system of intuitionistic set theory known as CZF, where L fails to exhibit such nice properties. We will demonstrate that, here, the theory C Z F + 𝑉 = 𝐿 is still equiconsistent with CZF, but the proof will involve a much more complicated realisability model and a recursion-theoretic argument.
Fields of Study & Subjects
Advanced Topology and Set Theory
Logic
programming
and type systems
Computability
AI Algorithms
Publication details
- Journal / source
- Annals of Pure and Applied Logic
- Volume
- 178
- Issue
- 3
- Pages
- 103842–103842
- Publication date
- 30 September 2026
- Language
- EN