Definability in terms of the successor function and the coprimeness predicate in the set of arbitrary integers
Journal of Symbolic Logic 54 (4):1253-1287 (1989)
| Abstract | Using coding devices based on a theorem due to Zsigmondy, Birkhoff and Vandiver, we first define in terms of successor S and coprimeness predicate $\perp$ a full arithmetic over the set of powers of some fixed prime, then we define in the same terms a restriction of the exponentiation. Hence we prove the main result insuring that all arithmetical relations and functions over prime powers and their opposite are $\{S, \perp\}$ -definable over Z. Applications to definability over Z and N are stated as corollaries of the main theorem | |||||||||
| Keywords | No keywords specified (fix it) | |||||||||
| Categories | ||||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,679 |
| External links |
 |
| Through your library | Configure |
Similar books and articlesJosé Iovino (1997). Definability in Functional Analysis. Journal of Symbolic Logic 62 (2):493-505.
Solomon Feferman (2010). Set-Theoretical Invariance Criteria for Logicality. Notre Dame Journal of Formal Logic 51 (1):3-20.
Michael Benedikt & H. Jerome Keisler (2003). Definability with a Predicate for a Semi-Linear Set. Journal of Symbolic Logic 68 (1):319-351.
Marius Petria & Răzvan Diaconescu (2006). Abstract Beth Definability in Institutions. Journal of Symbolic Logic 71 (3):1002 - 1028.
Alexis Bés & Denis Richard (1998). Undecidable Extensions of Skolem Arithmetic. Journal of Symbolic Logic 63 (2):379-401.
Denis Richard (1985). Answer to a Problem Raised by J. Robinson: The Arithmetic of Positive or Negative Integers is Definable From Successor and Divisibility. Journal of Symbolic Logic 50 (4):927-935.
Patrick Cegielski, Yuri Matiyasevich & Denis Richard (1996). Definability and Decidability Issues in Extensions of the Integers with the Divisibility Predicate. Journal of Symbolic Logic 61 (2):515-540.
Vladimir Kanovei (1996). On External Scott Algebras in Nonstandard Models of Peano Arithmetic. Journal of Symbolic Logic 61 (2):586-607.
Analytics
Monthly downloads
Sorry, there are not enough data points to plot this chart.
|
Added to index2009-01-28Total downloads2 ( #232,501 of 549,084 )Recent downloads (6 months)1 ( #63,317 of 549,084 )How can I increase my downloads? |
My notes
Discussion
