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  1. An axiomatic foundation of relativistic spacetime.Thomas Benda - 2015 - Synthese 192 (7):1-16.
    An ab-initio foundation for relativistic spacetime is given, which is a conservative extension of Zermelo’s set theory with urelemente. Primitive entities are worldlines rather than spacetime points. Spacetime points are sets of intersecting worldlines. By the proper axioms, they form a manifold. Entities known in differential geometry, up to a metric, are defined and have the usual properties. A set-realistic point of view is adopted. The intended ontology is a set-theoretical hierarchy with a broad base of the empty set and (...)
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  • David Hilbert. David Hilbert's lectures on the foundations of geometry, 1891–1902. Michael Hallett and Ulrich Majer, eds. David Hilbert's Foundational Lectures; 1. Berlin: Springer-Verlag, 2004. ISBN 3-540-64373-7. Pp. xxviii + 661. [REVIEW]V. Pambuccian - 2013 - Philosophia Mathematica 21 (2):255-277.
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  • On why-questions in physics.Gergely Székely - unknown
    In natural sciences, the most interesting and relevant questions are the so-called why-questions. There are several different approaches to why-questions and explanations in the literature, however, most of the literature deals with why-questions about particular events, such as ``Why did Adam eat the apple?''. Even the best known theory of explanation, Hempel's covering law model, is designed for explaining particular events. Here we only deal with purely theoretical why-questions about general phenomena of physics, for instance ``Why can no observer move (...)
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  • Investigations of isotropy and homogeneity of spacetime in first-order logic.Judit X. Madarász, Mike Stannett & Gergely Székely - 2022 - Annals of Pure and Applied Logic 173 (9):103153.
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  • Three different formalisations of einstein’s relativity principle.Judit X. Madarász, Gergely Székely & Mike Stannett - 2017 - Review of Symbolic Logic 10 (3):530-548.
    We present three natural but distinct formalisations of Einstein’s special principle of relativity, and demonstrate the relationships between them. In particular, we prove that they are logically distinct, but that they can be made equivalent by introducing a small number of additional, intuitively acceptable axioms.
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  • The existence of superluminal particles is consistent with relativistic dynamics.Judit X. Madarász & Gergely Székely - 2014 - Journal of Applied Logic 12 (4):477-500.
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  • Axiomatizing relativistic dynamics using formal thought experiments.Attila Molnár & Gergely Székely - 2015 - Synthese 192 (7):2183-2222.
    Thought experiments are widely used in the informal explanation of Relativity Theories; however, they are not present explicitly in formalized versions of Relativity Theory. In this paper, we present an axiom system of Special Relativity which is able to grasp thought experiments formally and explicitly. Moreover, using these thought experiments, we can provide an explicit definition of relativistic mass based only on kinematical concepts and we can geometrically prove the Mass Increase Formula in a natural way, without postulates of conservation (...)
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  • Motion and observation in a single-particle universe.Mike Stannett - 2015 - Synthese 192 (7):2261-2271.
    We outline an argument that a single-particle universe (a universe containing precisely one pointlike particle) can be described mathematically, in which observation can be considered meaningful despite the a priori impossibility of distinguishing between an observer and the observed. Moreover, we argue, such a universe can be observationally similar to the world we see around us. It is arguably impossible, therefore, to determine by experimental observation of the physical world whether the universe we inhabit contains one particle or many—modern scientific (...)
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