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

• Autorzy: Sitek Grzegorz
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

• Wydawca: Uniwersytet Mikołaja Kopernika (Nicolaus Copernicus University in Toruń)
• Czasopismo: Logic and Logical Philosophy
• Rocznik: 2017
• Tom: 26
• Numer: 4
• Strony: 531–562

Daty

wydano

2017-12-15

Twórcy

autor

Sitek Grzegorz

• Department of Logic, Faculty of Humanities, Nicolaus Copernicus University in Toruń, Poland ,
• Institute of Philosophy, Faculty of Philology and History, Jan Długosz University in Częstochowa, Poland

Bibliografia

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• Gruszczyński, R., and A. Pietruszczak, “Full development of Tarski’s geometry of solids”, The Bulletin of Symbolic Logic 14, 4 (2008): 481–540. DOI: 10.2178/bsl/1231081462
• Gruszczyński, R., and A. Pietruszczak, “Space, points and mereology. On foundations of point-free Euclidean geometry”, Logic and Logical Philosophy 18, 2 (2009): 145–188. DOI: 10.12775/LLP.2009.009
• Gruszczyński, R., and A. Pietruszczak, “How to define a mereological (collective) set”, Logic and Logical Philosophy 19, 4 (2010): 309–328. DOI: 10.12775/LLP.2010.011
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• Sitek, G., “Konstrukcje nowych pojęć w Tarskiego geometrii brył i ich zastosowanie w metaarytmetyce”, PhD thesis, Nicolaus Copernicus University in Toruń, 2016.
• Tarski, A., “Les fondements de la géometrié de corps”, pages 29–33 in Księga Pamiątkowa Pierwszego Polskiego Zjazdu Matematycznego, supplement to Annales de la Societé Polonaise de Mathématique, Kraków, 1929.
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Identyfikatory

DOI

10.12775/LLP.2017.016