Open Access
2016 Guessing, Mind-Changing, and the Second Ambiguous Class
Samuel Alexander
Notre Dame J. Formal Logic 57(2): 209-220 (2016). DOI: 10.1215/00294527-3443549


In his dissertation, Wadge defined a notion of guessability on subsets of the Baire space and gave two characterizations of guessable sets. A set is guessable if and only if it is in the second ambiguous class (Δ20), if and only if it is eventually annihilated by a certain remainder. We simplify this remainder and give a new proof of the latter equivalence. We then introduce a notion of guessing with an ordinal limit on how often one can change one’s mind. We show that for every ordinal α, a guessable set is annihilated by α applications of the simplified remainder if and only if it is guessable with fewer than α mind changes. We use guessability with fewer than α mind changes to give a semi-characterization of the Hausdorff difference hierarchy, and indicate how Wadge’s notion of guessability can be generalized to higher-order guessability, providing characterizations of Δα0 for all successor ordinals α>1.


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Samuel Alexander. "Guessing, Mind-Changing, and the Second Ambiguous Class." Notre Dame J. Formal Logic 57 (2) 209 - 220, 2016.


Received: 3 September 2013; Accepted: 8 January 2014; Published: 2016
First available in Project Euclid: 6 January 2016

zbMATH: 06585184
MathSciNet: MR3482743
Digital Object Identifier: 10.1215/00294527-3443549

Primary: 03E15

Keywords: descriptive hierarchy , difference hierarchy , guessability

Rights: Copyright © 2016 University of Notre Dame

Vol.57 • No. 2 • 2016
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