Defining integers
Bulletin of Symbolic Logic 17 (2):230-251 (2011)
| Abstract | This paper surveys the recent developments in the area that grew out of attempts to solve an analog of Hilbert's Tenth Problem for the field of rational numbers and the rings of integers of number fields. It is based on a plenary talk the author gave at the annual North American meeting of ASL at the University of Notre Dame in May of 2009 | |||||||||
| Keywords | No keywords specified (fix it) | |||||||||
| Categories | ||||||||||
| Options |
|
|||||||||
| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,701 |
| External links |
|
| Through your library | Configure |
Alexandra Shlapentokh (1992). A Diophantine Definition of Rational Integers Over Some Rings of Algebraic Numbers. Notre Dame Journal of Formal Logic 33 (3):299-321.
Alexandra Shlapentokh (2003). Existential Definability with Bounds on Archimedean Valuations. Journal of Symbolic Logic 68 (3):860-878.
Harvey Friedman, The Number of Certain Integral Polynomials and Nonrecursive Sets of Integers, Part.
Alexandra Shlapentokh (1993). Diophantine Relations Between Rings of s-Integers of Fields of Algebraic Functions in One Variable Over Constant Fields of Positive Characteristic. Journal of Symbolic Logic 58 (1):158-192.
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.
Alexandre Borovik, Renling Jin & Mikhail G. Katz (2012). An Integer Construction of Infinitesimals: Toward a Theory of Eudoxus Hyperreals. Notre Dame Journal of Formal Logic 53 (4):557-570.
Stewart Shapiro (2000). Frege Meets Dedekind: A Neologicist Treatment of Real Analysis. Notre Dame Journal of Formal Logic 41 (4):335--364.
Vladimir Kanovei (1996). On External Scott Algebras in Nonstandard Models of Peano Arithmetic. Journal of Symbolic Logic 61 (2):586-607.
Stephen Laurence & Eric Margolis (2005). Number and Natural Language. In Peter Carruthers, Stephen Laurence & Stephen P. Stich (eds.), The Innate Mind: Structure and Content. New York: Oxford University Press New York.
Jeremy Gwiazda (2006). The Train Paradox. Philosophia 34 (4):437-438.
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.
Monthly downloads |
Added to index2011-05-20Total downloads4 ( #178,675 of 549,090 )Recent downloads (6 months)0How can I increase my downloads? |

