Quantifier elimination for elementary geometry and elementary affine geometry

, &
Mathematical Logic Quarterly 58 (6):399-416 (2012)
  Copy   BIBTEX

Abstract

We introduce new first-order languages for the elementary n-dimensional geometry and elementary n-dimensional affine geometry , based on extending equation image and equation image, respectively, with new function symbols. Here, β stands for the betweenness relation and ≡ for the congruence relation. We show that the associated theories admit effective quantifier elimination

Categories

Keywords

Reprint years

DOI

10.1002/malq.201100095

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,783

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

Formalization of Hilbert's geometry of incidence and parallelism.Jan von Plato - 1997 - Synthese 110 (1):127-141.
Formalization of Hilbert's geometry of incidence and parallelism.Jan Platvono - 1997 - Synthese 110 (1):127-141.
Fourfold Geometry: being the Elementary Geometry of the Four-Dimensional World, By David Beveridge Mair. [REVIEW]T. P. Nunn - 1927 - Philosophy 2 (5):113.
A consistency proof for elementary algebra and geometry.Harvey Friedman - manuscript
Quantifier-free axioms for constructive affine plane geometry.Patrick Suppes - 2000 - Synthese 125 (1-2):263-281.
T-Convexity and Tame Extensions.Dries Lou Van Den & H. Lewenberg Adam - 1995 - Journal of Symbolic Logic 60 (1):74 - 102.
T-convexity and Tame extensions.LouDen Dries & Adam H. Lewenberg - 1995 - Journal of Symbolic Logic 60 (1):74 - 102.
Axiomatizations of hyperbolic geometry: A comparison based on language and quantifier type complexity.Victor Pambuccian - 2002 - Synthese 133 (3):331 - 341.
Remarks on the geometry of visibles.Gordon Belot - 2003 - Philosophical Quarterly 53 (213):581–586.
Jakościowe teorie czasoprzestrzeni.Tomasz Bigaj - 1995 - Filozofia Nauki 4.
The application of mereology to grounding of elementary geometry.Edmund Glibowski - 1969 - Studia Logica 24 (1):109-129.
Quantifier Elimination for the Reals with a Predicate for the Powers of Two.Jeremy Avigad & Yimu Yin - unknown
An enhanced argument for innate elementary geometric knowledge and its philosophical implications.Helen3 De Cruz - 2007 - In Bart Van Kerkhove (ed.), New perspectives on mathematical practices. Essays in philosophy and history of mathematics. World Scientific.
The Ackermann function in elementary algebraic geometry.Harvey Friedman - manuscript
The completeness of elementary algebra and geometry.Alfred Tarski - 1967 - Paris,: Centre national de la recherche scientifique, Institut Blaise Pascal.

Analytics

Added to PP
2013-10-31

Downloads
39 (#407,668)

6 months
11 (#235,184)

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

Mathematical logic.Joseph R. Shoenfield - 1967 - Reading, Mass.,: Addison-Wesley.
A Decision Method for Elementary Algebra and Geometry.Alfred Tarski - 1952 - Journal of Symbolic Logic 17 (3):207-207.
A Decision Method for Elementary Algebra and Geometry.Alfred Tarski - 1949 - Journal of Symbolic Logic 14 (3):188-188.
Tarski's system of geometry.Alfred Tarski & Steven Givant - 1999 - Bulletin of Symbolic Logic 5 (2):175-214.

View all 10 references / Add more references