Notre Dame Journal of Formal Logic

Weak Truth Table Degrees of Structures

David R. Belanger

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Abstract

We study the weak truth table (wtt) degree spectra of first-order relational structures. We prove a dichotomy among the possible wtt degree spectra along the lines of Knight’s upward-closure theorem for Turing degree spectra. We prove new results contrasting the wtt degree spectra of finite- and infinite-signature structures. We show that, as a method of defining classes of reals, the wtt degree spectrum is, except for some trivial cases, strictly more expressive than the Turing degree spectrum.

Article information

Source
Notre Dame J. Formal Logic, Volume 56, Number 2 (2015), 263-285.

Dates
First available in Project Euclid: 17 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1429277351

Digital Object Identifier
doi:10.1215/00294527-2864298

Mathematical Reviews number (MathSciNet)
MR3337380

Zentralblatt MATH identifier
1334.03041

Subjects
Primary: 03D45: Theory of numerations, effectively presented structures [See also 03C57; for intuitionistic and similar approaches see 03F55]
Secondary: 03D30: Other degrees and reducibilities

Keywords
degree spectra of structures weak truth table degrees

Citation

Belanger, David R. Weak Truth Table Degrees of Structures. Notre Dame J. Formal Logic 56 (2015), no. 2, 263--285. doi:10.1215/00294527-2864298. https://projecteuclid.org/euclid.ndjfl/1429277351


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