Games with 1-backtracking
Journal article, 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.

Learning in the limit

Recursive degree

Classical logic



Limit computable

Game semantics


S. Berardi

University of Turin

Thierry Coquand

Chalmers, Computer Science and Engineering (Chalmers), Computing Science (Chalmers)

S. Hayashi

Kyoto University

Annals of Pure and Applied Logic

0168-0072 (ISSN)

Vol. 161 10 1254-1269

Subject Categories

Other Mathematics



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