Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/14864
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dc.contributor.authorGRIMSON, Rafael-
dc.contributor.authorKUIJPERS, Bart-
dc.contributor.authorOTHMAN, Walied-
dc.date.accessioned2013-03-29T10:45:26Z-
dc.date.available2013-03-29T10:45:26Z-
dc.date.issued2012-
dc.identifier.citationMathematical Logic Quarterly, 58 (6), p. 399-416-
dc.identifier.issn0942-5616-
dc.identifier.urihttp://hdl.handle.net/1942/14864-
dc.description.abstractWe introduce new first-order languages for the elementary n-dimensional geometry and elementary n-dimensional affine geometry (n ≥ 2), based on extending FO(β,≡) and FO(β), 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.-
dc.description.sponsorshipFWO G.0344.05-
dc.language.isoen-
dc.rightsJournal (Mathematical Logic Quarterly) copyright-
dc.subject.otherLogic; Databases; Geometry; Quantifier elimination-
dc.titleQuantifier elimination for elementary geometry and elementary affine geometry-
dc.typeJournal Contribution-
dc.identifier.epage416-
dc.identifier.issue6-
dc.identifier.spage399-
dc.identifier.volume58-
local.bibliographicCitation.jcatA1-
dc.description.notes[Grimson, Rafael] Univ Buenos Aires, Dept Matemat, Fac Ciencias Exactas & Nat, Buenos Aires, DF, Argentina. [Kuijpers, Bart] Hasselt Univ, Theoret Comp Sci Grp, B-3590 Diepenbeek, Belgium. [Kuijpers, Bart] Transnat Univ Limburg, B-3590 Diepenbeek, Belgium. [Othman, Walied] Univ Zurich, Inst Geog, CH-8057 Zurich, Switzerland.-
dc.relation.referencesMarco Aiello, Ian E. Pratt-Hartmann, and Johan F.A.K. van Ben- them, Handbook of spatial logics, ch. Logical theories for fragments of elementary geometry, pp. 343–428, Springer-Verlag New York, Inc., Secaucus, NJ, USA, 2007. J. Bochnak, M. Coste, and M. F. Roy, Real algebraic geometry, Springer-Verlag, 1998. S. Basu, R. Pollack, and M. F. Roy, Algorithms in real algebraic geometry (algorithms and computation in mathematics), Springer- Verlag New York, Inc., Secaucus, NJ, USA, 2006. R. Descartes, La g ́eom ́etrie, Jan Maire, Laiden, 1637. H. Enderton, A mathematical introduction to logic, Harcourt/Academic Press, 2000. M. Gyssens, J. Van den Bussche, and D. Van Gucht, Complete geo- metric query languages, Journal of Computer and System Sciences 58 (1999), no. 3, 483–511. R. Hartshorne, Geometry: Euclid and beyond, Springer, 2000. D. Hilbert, Foundations of geometry, Open Court, La Salle, 1971. G. Kuper, L. Libkin, and J. Paredaens, Constraint Databases, Springer-Verlag, 2000. D. Marker, Model theory: an introduction, Graduate texts in math- ematics, Springer, 2002. N. Moler and P. Suppes, Quantifier-free axioms for constructive plane geometry, Compositio Math. 20 (1968), 143–152. V. Pambuccian, Constructive axiomatizations of plane absolute, eu- clidean and hyperbolic geometry, Math. Log. Q. 47 (2001), no. 1, 129–136. V. Pambuccian,, Axiomatizing geometric constructions, J. Applied Logic 6 (2008), no. 1, 24–46. B. Poizat, A course in model theory: an introduction to contempo- rary mathematical logic, Universitext Series, Springer, 2000. Wolfram Schwabh ̈auser, U ̈ber die vollst ̈andigkeit der elementaren euklidischen geometrie, Mathematical Logic Quarterly 2 (1956), no. 10-15, 137–165. J. Shoenfield, Mathematical logic, Addison-Wesley, 1967. L. Szczebra and A. Tarski, Metamathematical discussion of some affine geometries, Fundamenta Mathematicae 104 (1979), 155–192. W. Szmielew, From affine to euclidean geometry. An axiomatic approach, Kluwer Academic Publishers, The Netherlands, 1983. A. Tarski, Sur les ensembles d ́efinissables de nombres r ́eels, Funda- menta Mathematicae 17 (1931), 210–239. A. Tarski, A decision method for elementary algebra and geometry, second ed., Univ. of California Press, Berkley, CA, 1951. A. Tarski, The axiomatic method (with special reference to geometry and physics), ch. What is elementary geometry?, pp. 16–29, North- Holland, Amsterdam, 1959. A. Tarski and S. Givant, Tarski’s system of geometry, Bull. Sym- bolic Logic 5 (1999), 175–214. O. Veblen, A system of axioms for geometry, Transaction of the American Mathematical Society 5 (1904), 343–384. W. Szmielew W. Schwabh ̈auser and A. Tarski, Metamathematische Methoden in der Geometrie, Springer-Verlag, 1983. 28-
local.type.refereedRefereed-
local.type.specifiedArticle-
local.relation.fp7245410-
dc.identifier.doi10.1002/malq.201100095-
dc.identifier.isi000310973400006-
item.contributorGRIMSON, Rafael-
item.contributorKUIJPERS, Bart-
item.contributorOTHMAN, Walied-
item.fulltextWith Fulltext-
item.validationecoom 2014-
item.fullcitationGRIMSON, Rafael; KUIJPERS, Bart & OTHMAN, Walied (2012) Quantifier elimination for elementary geometry and elementary affine geometry. In: Mathematical Logic Quarterly, 58 (6), p. 399-416.-
item.accessRightsRestricted Access-
crisitem.journal.issn0942-5616-
crisitem.journal.eissn1521-3870-
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