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September 2008 Selection in the monadic theory of a countable ordinal
Alexander Rabinovich, Amit Shomrat
J. Symbolic Logic 73(3): 783-816 (September 2008). DOI: 10.2178/jsl/1230396747

Abstract

A monadic formula ψ(Y) is a selector for a formula φ(Y) in a structure ℳ if there exists a unique subset P of ℳ which satisfies ψ and this P also satisfies φ. We show that for every ordinal α≥ ωω there are formulas having no selector in the structure (α, <). For α ≤ ω1, we decide which formulas have a selector in (α, <), and construct selectors for them. We deduce the impossibility of a full generalization of the Büchi-Landweber solvability theorem from (ω, <) to (ωω, <). We state a partial extension of that theorem to all countable ordinals. To each formula we assign a selection degree which measures “how difficult it is to select”. We show that in a countable ordinal all non-selectable formulas share the same degree.

Citation

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Alexander Rabinovich. Amit Shomrat. "Selection in the monadic theory of a countable ordinal." J. Symbolic Logic 73 (3) 783 - 816, September 2008. https://doi.org/10.2178/jsl/1230396747

Information

Published: September 2008
First available in Project Euclid: 27 December 2008

zbMATH: 1163.03013
MathSciNet: MR2444268
Digital Object Identifier: 10.2178/jsl/1230396747

Rights: Copyright © 2008 Association for Symbolic Logic

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Vol.73 • No. 3 • September 2008
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