Fixpoints, games and the difference hierarchy
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 37 (2003) no. 1, pp. 1-15.

Drawing on an analogy with temporal fixpoint logic, we relate the arithmetic fixpoint definable sets to the winning positions of certain games, namely games whose winning conditions lie in the difference hierarchy over ${\Sigma }_{2}^{0}$. This both provides a simple characterization of the fixpoint hierarchy, and refines existing results on the power of the game quantifier in descriptive set theory. We raise the problem of transfinite fixpoint hierarchies.

DOI : https://doi.org/10.1051/ita:2003011
Classification : 03E15,  68Q45
Mots clés : descriptive set theory, fixpoint, game quantifier, induction
@article{ITA_2003__37_1_1_0,
title = {Fixpoints, games and the difference hierarchy},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {1--15},
publisher = {EDP-Sciences},
volume = {37},
number = {1},
year = {2003},
doi = {10.1051/ita:2003011},
zbl = {1043.03038},
mrnumber = {1991748},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ita:2003011/}
}
Bradfield, Julian C. Fixpoints, games and the difference hierarchy. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 37 (2003) no. 1, pp. 1-15. doi : 10.1051/ita:2003011. http://www.numdam.org/articles/10.1051/ita:2003011/

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