Hilbert's 17th Problem for Real Closed Rings

Mathematical Logic Quarterly 40 (4):445-454 (1994)
  Copy   BIBTEX

Abstract

We recall the characterisation of positive definite polynomial functions over a real closed ring due to Dickmann, and give a new proof of this result, based upon ideas of Abraham Robinson. In addition we isolate the class of convexly ordered valuation rings for which this characterisation holds

Categories

Keywords

Reprint years

DOI

10.1002/malq.19940400403

Other Versions

No versions found

Links

PhilArchive

    This entry is not archived by us. If you are the author and have permission from the publisher, we recommend that you archive it. Many publishers automatically grant permission to authors to archive pre-prints. By uploading a copy of your work, you will enable us to better index it, making it easier to find.

    Upload a copy of this work     Papers currently archived: 102,964

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Completions of Convexly Ordered Valuation Rings.Larry Mathews - 1994 - Mathematical Logic Quarterly 40 (3):318-330.
Real closed rings and ordered valuation ring.Thomas Becker - 1983 - Mathematical Logic Quarterly 29 (8):417-425.
Strongly NIP almost real closed fields.Lothar Sebastian Krapp, Salma Kuhlmann & Gabriel Lehéricy - 2021 - Mathematical Logic Quarterly 67 (3):321-328.
Existentially closed ordered difference fields and rings.Françoise Point - 2010 - Mathematical Logic Quarterly 56 (3):239-256.
Boolean products of real closed valuation rings and fields.Jorge I. Guier - 2001 - Annals of Pure and Applied Logic 112 (2-3):119-150.
Some model theory for almost real closed fields.Francoise Delon & Rafel Farre - 1996 - Journal of Symbolic Logic 61 (4):1121-1152.
Interpreting arithmetic in the first-order theory of addition and coprimality of polynomial rings.Javier Utreras - 2019 - Journal of Symbolic Logic 84 (3):1194-1214.
Ganzstellensätze in theories of valued fields.Deirdre Haskell & Yoav Yaffe - 2008 - Journal of Mathematical Logic 8 (1):1-22.
The strong soundness theorem for real closed fields and Hilbert’s Nullstellensatz in second order arithmetic.Nobuyuki Sakamoto & Kazuyuki Tanaka - 2004 - Archive for Mathematical Logic 43 (3):337-349.

Analytics

Added to PP
2013-12-01

Downloads
21 (#1,041,718)

6 months
3 (#1,090,149)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

A Decision Method for Elementary Algebra and Geometry.Alfred Tarski - 1952 - Journal of Symbolic Logic 17 (3):207-207.
Real closed rings II. model theory.Gregory Cherlin & Max A. Dickmann - 1983 - Annals of Pure and Applied Logic 25 (3):213-231.
Cardinal Algebras.Alfred Tarski & Bjarni Jonsson - 1949 - Journal of Symbolic Logic 14 (3):188-189.
Real closed rings and ordered valuation ring.Thomas Becker - 1983 - Mathematical Logic Quarterly 29 (8):417-425.

View all 7 references / Add more references