The Notion of the Diameter of Mereological Ball in Tarski's Geometry of Solids

Grzegorz Sitek

doi:10.12775/LLP.2017.016

Authors

Grzegorz Sitek Nicolaus Copernicus University in Toruń

DOI:

https://doi.org/10.12775/LLP.2017.016

Keywords

Tarski’s geometry of solids, mereology, diameter of mereological ball, congruence of mereological balls, point-free geometry

Abstract

In the paper "Full development of Tarski's geometry of solids" Gruszczyński and Pietruszczak have obtained the full development of Tarski’s geometry of solids that was sketched in [14, 15]. In this paper 1 we introduce in Tarski’s theory the notion of congruence of mereological balls and then the notion of diameter of mereological ball. We prove many facts about these new concepts, e.g., we give a characterization of mereological balls in terms of its center and diameter and we prove that the set of all diameters together with the relation of inequality of diameters is the dense linearly ordered set without the least and the greatest element.

Author Biography

Grzegorz Sitek, Nicolaus Copernicus University in Toruń

Department of Logic, Faculty of Humanities

References

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