March 2011 Computability of Fraïssé limits
Barbara F. Csima, Valentina S. Harizanov, Russell Miller, Antonio Montalbán
J. Symbolic Logic 76(1): 66-93 (March 2011). DOI: 10.2178/jsl/1294170990

Abstract

Fraïssé studied countable structures 𝒮 through analysis of the age of 𝒮, i.e., the set of all finitely generated substructures of 𝒮. We investigate the effectiveness of his analysis, considering effectively presented lists of finitely generated structures and asking when such a list is the age of a computable structure. We focus particularly on the Fraïssé limit. We also show that degree spectra of relations on a sufficiently nice Fraïssé limit are always upward closed unless the relation is definable by a quantifier-free formula. We give some sufficient or necessary conditions for a Fraïssé limit to be spectrally universal. As an application, we prove that the computable atomless Boolean algebra is spectrally universal.

Citation

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Barbara F. Csima. Valentina S. Harizanov. Russell Miller. Antonio Montalbán. "Computability of Fraïssé limits." J. Symbolic Logic 76 (1) 66 - 93, March 2011. https://doi.org/10.2178/jsl/1294170990

Information

Published: March 2011
First available in Project Euclid: 4 January 2011

zbMATH: 1215.03053
MathSciNet: MR2791338
Digital Object Identifier: 10.2178/jsl/1294170990

Rights: Copyright © 2011 Association for Symbolic Logic

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Vol.76 • No. 1 • March 2011
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