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

Grzegorz Sitek

doi:10.12775/LLP.2017.016

Autor

Grzegorz Sitek Uniwersytet Mikołaja Kopernika w Toruniu Wydział Humanistyczny Katedra Logiki

DOI:

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

Słowa kluczowe

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

Abstrakt

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.

Biogram autora

Grzegorz Sitek - Uniwersytet Mikołaja Kopernika w Toruniu Wydział Humanistyczny Katedra Logiki

Department of Logic, Faculty of Humanities

Bibliografia

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