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  1. How to Define a Mereological (Collective) Set.Rafał Gruszczyński & Andrzej Pietruszczak - 2010 - Logic and Logical Philosophy 19 (4):309-328.
    As it is indicated in the title, this paper is devoted to the problem of defining mereological (collective) sets. Starting from basic properties of sets in mathematics and differences between them and so called conglomerates in Section 1, we go on to explicate informally in Section 2 what it means to join many objects into a single entity from point of view of mereology, the theory of part of (parthood) relation. In Section 3 we present and motivate basic axioms for (...)
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  2. Space, Points and Mereology. On Foundations of Point-Free Euclidean Geometry.Rafał Gruszczyński & Andrzej Pietruszczak - 2009 - Logic and Logical Philosophy 18 (2):145-188.
    This article is devoted to the problem of ontological foundations of three-dimensional Euclidean geometry. Starting from Bertrand Russell’s intuitions concerning the sensual world we try to show that it is possible to build a foundation for pure geometry by means of the so called regions of space. It is not our intention to present mathematically developed theory, but rather demonstrate basic assumptions, tools and techniques that are used in construction of systems of point-free geometry and topology by means of mereology (...)
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  3.  27
    Mereology Then and Now.Rafał Gruszczyński & Achille C. Varzi - 2015 - Logic and Logical Philosophy 24 (4):409.
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  4.  11
    Parts of Falling Objects: Galileo’s Thought Experiment in Mereological Setting.Rafał Gruszczyński - forthcoming - Erkenntnis:1-22.
    This paper aims to formalize Galileo’s argument against the Aristotelian view that the weight of free-falling bodies influences their speed. I obtain this via the application of concepts of parthood and of mereological sum, and via recognition of a principle which is not explicitly formulated by the Italian thinker but seems to be natural and helpful in understanding the logical mechanism behind Galileo’s train of thought. I also compare my reconstruction to one of those put forward by Atkinson and Peijnenburg (...)
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  5.  6
    A Study in Grzegorczyk Point-Free Topology Part I: Separation and Grzegorczyk Structures.Rafał Gruszczyński & Andrzej Pietruszczak - 2018 - Studia Logica 106 (6):1197-1238.
    This is the first, out of two papers, devoted to Andrzej Grzegorczyk’s point-free system of topology from Grzegorczyk :228–235, 1960. https://doi.org/10.1007/BF00485101). His system was one of the very first fully fledged axiomatizations of topology based on the notions of region, parthood and separation. Its peculiar and interesting feature is the definition of point, whose intention is to grasp our geometrical intuitions of points as systems of shrinking regions of space. In this part we analyze separation structures and Grzegorczyk structures, and (...)
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  6.  39
    Full Development of Tarski's Geometry of Solids.Rafał Gruszczyński & Andrzej Pietruszczak - 2008 - Bulletin of Symbolic Logic 14 (4):481-540.
    In this paper we give probably an exhaustive analysis of the geometry of solids which was sketched by Tarski in his short paper [20, 21]. We show that in order to prove theorems stated in [20, 21] one must enrich Tarski's theory with a new postulate asserting that the universe of discourse of the geometry of solids coincides with arbitrary mereological sums of balls, i.e., with solids. We show that once having adopted such a solution Tarski's Postulate 4 can be (...)
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  7.  10
    A Study in Grzegorczyk Point-Free Topology Part II: Spaces of Points.Rafał Gruszczyński & Andrzej Pietruszczak - 2019 - Studia Logica 107 (4):809-843.
    In the second installment to Gruszczyński and Pietruszczak we carry out an analysis of spaces of points of Grzegorczyk structures. At the outset we introduce notions of a concentric and \-concentric topological space and we recollect some facts proven in the first part which are important for the sequel. Theorem 2.9 is a strengthening of Theorem 5.13, as we obtain stronger conclusion weakening Tychonoff separation axiom to mere regularity. This leads to a stronger version of Theorem 6.10. Further, we show (...)
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  8.  4
    A Comparison of Two Systems of Point-Free Topology.Rafał Gruszczyński & Andrzej Pietruszczak - 2018 - Bulletin of the Section of Logic 47 (3):187.
    This is a spin-off paper to [3, 4] in which we carried out an extensive analysis of Andrzej Grzegorczyk’s point-free topology from [5]. In [1] Loredana Biacino and Giangiacomo Gerla presented an axiomatization which was inspired by the Grzegorczyk’s system, and which is its variation. Our aim is to compare the two approaches and show that they are slightly different. Except for pointing to dissimilarities, we also demonstrate that the theories coincide in presence of axiom stipulating non-existence of atoms.
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  9.  9
    Point-Free Geometry, Ovals, and Half-Planes.Giangiacomo Gerla & Rafał Gruszczyński - 2017 - Review of Symbolic Logic 10 (2):237-258.
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