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2003 Embedding and Coding below a 1-Generic Degree
Noam Greenberg, Antonio Montalbán
Notre Dame J. Formal Logic 44(4): 200-216 (2003). DOI: 10.1305/ndjfl/1091122498

Abstract

We show that the theory of 𝒟(≤ g), where g is a 2-generic or a 1-generic degree below 0ʹ, interprets true first-order arithmetic. To this end we show that 1-genericity is sufficient to find the parameters needed to code a set of degrees using Slaman and Woodin's method of coding in Turing degrees. We also prove that any recursive lattice can be embedded below a 1-generic degree preserving top and bottom.

Citation

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Noam Greenberg. Antonio Montalbán. "Embedding and Coding below a 1-Generic Degree." Notre Dame J. Formal Logic 44 (4) 200 - 216, 2003. https://doi.org/10.1305/ndjfl/1091122498

Information

Published: 2003
First available in Project Euclid: 29 July 2004

zbMATH: 1066.03045
MathSciNet: MR2130306
Digital Object Identifier: 10.1305/ndjfl/1091122498

Subjects:
Primary: 03D28, 03D35

Rights: Copyright © 2003 University of Notre Dame

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Vol.44 • No. 4 • 2003
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