Journal of Symbolic Logic

Computability of Fraïssé limits

Barbara F. Csima, Valentina S. Harizanov, Russell Miller, and Antonio Montalbán

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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.

Article information

Source
J. Symbolic Logic, Volume 76, Issue 1 (2011), 66-93.

Dates
First available in Project Euclid: 4 January 2011

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1294170990

Digital Object Identifier
doi:10.2178/jsl/1294170990

Mathematical Reviews number (MathSciNet)
MR2791338

Zentralblatt MATH identifier
1215.03053

Citation

Csima, Barbara F.; Harizanov, Valentina S.; Miller, Russell; Montalbán, Antonio. Computability of Fraïssé limits. J. Symbolic Logic 76 (2011), no. 1, 66--93. doi:10.2178/jsl/1294170990. https://projecteuclid.org/euclid.jsl/1294170990


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