Journal of Symbolic Logic 72 (1):305 - 323 (2007)

Authors
Valentina Harizanov
George Washington University
Abstract
A Turing degree d is homogeneous bounding if every complete decidable (CD) theory has a d-decidable homogeneous model A, i.e., the elementary diagram De (A) has degree d. It follows from results of Macintyre and Marker that every PA degree (i.e., every degree of a complete extension of Peano Arithmetic) is homogeneous bounding. We prove that in fact a degree is homogeneous bounding if and only if it is a PA degree. We do this by showing that there is a single CD theory T such that every homogeneous model of T has a PA degree
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2178/jsl/1174668397
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 53,682
Through your library

References found in this work BETA

Degrees Coded in Jumps of Orderings.Julia F. Knight - 1986 - Journal of Symbolic Logic 51 (4):1034-1042.
Foundations of Recursive Model Theory.Terrence S. Millar - 1978 - Annals of Pure and Applied Logic 13 (1):45.
Recursively Presentable Prime Models.Leo Harrington - 1974 - Journal of Symbolic Logic 39 (2):305-309.

View all 10 references / Add more references

Citations of this work BETA

The Degree Spectra of Homogeneous Models.Karen Lange - 2008 - Journal of Symbolic Logic 73 (3):1009-1028.

Add more citations

Similar books and articles

Bounding Prime Models.Barbara F. Csima, Denis R. Hirschfeldt, Julia F. Knight & Robert I. Soare - 2004 - Journal of Symbolic Logic 69 (4):1117 - 1142.
A Characterization of the 0 -Basis Homogeneous Bounding Degrees.Karen Lange - 2010 - Journal of Symbolic Logic 75 (3):971-995.
Computability of Homogeneous Models.Karen Lange & Robert I. Soare - 2007 - Notre Dame Journal of Formal Logic 48 (1):143-170.
On the Number of Countable Homogeneous Models.Libo Lo - 1983 - Journal of Symbolic Logic 48 (3):539-541.
Saturation of Homogeneous Resplendent Models.Julia F. Knight - 1986 - Journal of Symbolic Logic 51 (1):222-224.
The Degree Spectra of Homogeneous Models.Karen Lange - 2008 - Journal of Symbolic Logic 73 (3):1009-1028.
Morley Rank in Homogeneous Models.Alexei Kolesnikov & G. V. N. G. Krishnamurthi - 2006 - Notre Dame Journal of Formal Logic 47 (3):319-329.
The Spectrum of Resplendency.John T. Baldwin - 1990 - Journal of Symbolic Logic 55 (2):626-636.

Analytics

Added to PP index
2010-08-24

Total views
33 ( #298,656 of 2,349,382 )

Recent downloads (6 months)
1 ( #510,581 of 2,349,382 )

How can I increase my downloads?

Downloads

My notes