Possible m-diagrams of models of arithmetic
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)|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Degree Spectra of Prime Models.Barbara F. Csima - 2004 - Journal of Symbolic Logic 69 (2):430 - 442.
Models of Arithmetic and Upper Bounds for Arithmetic Sets.Alistair H. Lachlan & Robert I. Soare - 1994 - Journal of Symbolic Logic 59 (3):977-983.
Theories of Arithmetics in Finite Models.M. Krynicki & K. Zdanowski - 2005 - Journal of Symbolic Logic 70 (1):1-28.
Inconsistent Models of Arithmetic Part I: Finite Models. [REVIEW]Graham Priest - 1997 - Journal of Philosophical Logic 26 (2):223-235.
The Complexity of Classification Problems for Models of Arithmetic.Samuel Coskey & Roman Kossak - 2010 - Bulletin of Symbolic Logic 16 (3):345-358.
Diagrams as Locality Aids for Explanation and Model Construction in Cell Biology.Nicholaos Jones & Olaf Wolkenhauer - 2012 - Biology and Philosophy 27 (5):705-721.
On the Complexity of Models of Arithmetic.Kenneth McAloon - 1982 - Journal of Symbolic Logic 47 (2):403-415.
On Certain Types and Models for Arithmetic.Andreas Blass - 1974 - Journal of Symbolic Logic 39 (1):151-162.
Local Definitions in Degeree Structures: The Turing Jump, Hyperdegrees and Beyond.Richard A. Shore - 2007 - Bulletin of Symbolic Logic 13 (2):226-239.
Added to index2009-01-28
Total downloads6 ( #555,530 of 2,164,249 )
Recent downloads (6 months)0
How can I increase my downloads?