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Interpreting true arithmetic in the -enumeration degrees

Published online by Cambridge University Press:  12 March 2014

Thomas F. Kent
Thomas F. Kent*
Affiliation:
Department of Mathematics, Marywood University, 2300 Adams Avenue, Scranton, Pa 18509, USA. E-mail: tfkent@marywood.edu
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Abstract

We show that there is a first order sentence φ(x: a, b, l) such that for every computable partial order and -degree u > 0e, there are -enumeration degrees a ≤ u, b, and l such that . Allowing to be a suitably defined standard model of arithmetic gives a parameterized interpretation of true arithmetic in the -enumeration degrees. Finally we show that there is a first order sentence that correctly identifies a subset of the standard models, which gives a parameterless interpretation of true arithmetic in the -enumeration degrees.

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Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 2 , June 2010, pp. 522 - 550
Copyright
Copyright © Association for Symbolic Logic 2010

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