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POINT-FREE GEOMETRY, OVALS, AND HALF-PLANES

  • GIANGIACOMO GERLA (a1) and RAFAŁ GRUSZCZYŃSKI (a2)
Abstract
Abstract

In this paper we develop a point-free system of geometry based on the notions of region, parthood, and ovality, the last one being a region-based counterpart of the notion of convex set. In order to show that the system we propose is sufficient to reconstruct an affine geometry we make use of a theory of a Polish mathematician Aleksander Śniatycki from [15], in which the concept of half-plane is assumed as basic.

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*THE INTERNATIONAL INSTITUTE FOR ADVANCED SCIENTIFIC STUDIES (IIASS) SALERNO, ITALY E-mail: ggerla104@gmail.comURL: www.ggerla.it
DEPARTMENT OF LOGIC NICOLAUS COPERNICUS UNIVERSITY IN TORUŃ POLAND E-mail: gruszka@umk.plURL: www.umk.pl/∼gruszka
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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

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M. L. J van de Vel . (1993). Theory of Convex Structures. Amsterdam: North-Holland.

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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
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