Peano arithmetic, games and descent recursion
Year: 2024
Type: article
Abstract: We analyze Coquand's game-theoretic interpretation of Peano Arithmetic through the lens of elementary descent recursion. In Coquand's game semantics, winning strategies correspond to infinitary cut-free proofs and cut elimination corresponds to debates between these winning strategies. The proof of cut elimination, i.e., the proof that such debates eventually terminate, is by transfinite induction on certain interaction sequences of ordinals. In this paper, we provide a direct implementation of Coquand's proof, one that allows us to describe winning strategies by descent recursive functions. As a byproduct, we obtain yet another proof of well-known results about provably recursive functions and functionals.
Source: Annals of Pure and Applied Logic
Author: Emanuele Frittaion
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,420
Funder: Alexander von Humboldt-Stiftung
OpenAlex ID: W4405317105