Games with 1-backtracking
Artikel i vetenskaplig tidskrift, 2010

We associate with any game G another game, which is a variant of it, and which we call bck(G). Winning strategies for bck(G) have a lower recursive degree than winning strategies for G: if a player has a winning strategy of recursive degree 1 over G, then it has a recursive winning strategy over bck(G), and vice versa. Through bck(G) we can express in algorithmic form, as a recursive winning strategy, many (but not all) common proofs of non-constructive Mathematics, namely exactly the theorems of the sub-classical logic Limit Computable Mathematics (Hayashi (2006) [6], Hayashi and Nakata (2001) [7]). (C) 2010 Elsevier B.V. All rights reserved.

Limit computable

Recursive degree

Game semantics

Learning in the limit


Classical logic



S. Berardi

Universita degli Studi di Torino

Thierry Coquand

Chalmers, Data- och informationsteknik, Datavetenskap

S. Hayashi

Kyoto University

Annals of Pure and Applied Logic

0168-0072 (ISSN)

Vol. 161 1254-1269


Annan matematik