Year: 2026
Type: preprint
Abstract: It is known, by works of Werner and Carneiro, that the type theory of Lean (and indeed of CIC plus a version of choice) is equiconsistent with ZFC plus "there are infinitely many strongly inaccessible cardinals". We prove a finer connection between these two formal systems; namely, given any formula in the language of second order arithmetic, that formula is provable in the aforementioned extension of ZFC if and only if the same formula, when viewed as a type in Lean, is inhabited.
Source: arXiv (Cornell University)
Authors: Bresolin, Lorenzo, Mamino, Marcello
Institution: University of Pisa
Language: English
Subfield: Software
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223277581