Possible m-diagrams of models of arithmetic
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
In Stephen Simpson (ed.), Reverse Mathematics 2001 (2005)
In this paper I begin by extending two results of Solovay; the first characterizes the possible Turing degrees of models of True Arithmetic (TA), the complete first-order theory of the standard model of PA, while the second characterizes the possible Turing degrees of arbitrary completions of P. I extend these two results to characterize the possible Turing degrees of m-diagrams of models of TA and of arbitrary complete extensions of PA. I next give a construction showing that the conditions Solovay identified for his characterization of degrees of models of arbitrary completions of PA cannot be dropped (I showed that these conditions cannot be simplified in the paper.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Barbara F. Csima (2004). Degree Spectra of Prime Models. Journal of Symbolic Logic 69 (2):430 - 442.
Richard A. Shore (2007). Local Definitions in Degeree Structures: The Turing Jump, Hyperdegrees and Beyond. Bulletin of Symbolic Logic 13 (2):226-239.
Andreas Blass (1974). On Certain Types and Models for Arithmetic. Journal of Symbolic Logic 39 (1):151-162.
Kenneth McAloon (1982). On the Complexity of Models of Arithmetic. Journal of Symbolic Logic 47 (2):403-415.
Nicholaos Jones & Olaf Wolkenhauer (2012). Diagrams as Locality Aids for Explanation and Model Construction in Cell Biology. Biology and Philosophy 27 (5):705-721.
Samuel Coskey & Roman Kossak (2010). The Complexity of Classification Problems for Models of Arithmetic. Bulletin of Symbolic Logic 16 (3):345-358.
Graham Priest (1997). Inconsistent Models of Arithmetic Part I: Finite Models. [REVIEW] Journal of Philosophical Logic 26 (2):223-235.
M. Krynicki & K. Zdanowski (2005). Theories of Arithmetics in Finite Models. Journal of Symbolic Logic 70 (1):1-28.
Alistair H. Lachlan & Robert I. Soare (1994). Models of Arithmetic and Upper Bounds for Arithmetic Sets. Journal of Symbolic Logic 59 (3):977-983.
Andrew Arana (2001). Solovay's Theorem Cannot Be Simplified. Annals of Pure and Applied Logic 112 (1):27-41.
Added to index2009-01-28
Total downloads6 ( #206,643 of 1,102,718 )
Recent downloads (6 months)0
How can I increase my downloads?