A formal construction of the spacetime manifold

Journal of Philosophical Logic 37 (5):441 - 478 (2008)
Abstract
The spacetime manifold, the stage on which physics is played, is constructed ab initio in a formal program that resembles the logicist reconstruction of mathematics. Zermelo’s set theory extended by urelemente serves as a framework, to which physically interpretable proper axioms are added. From this basis, a topology and subsequently a Hausdorff manifold are readily constructed which bear the properties of the known spacetime manifold. The present approach takes worldlines rather than spacetime points to be primitive, having them represented by urelemente. Thereby it is demonstrated that an important part of physics is formally reducible to set theory.
Keywords axiomatization  general relativity  spacetime
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References found in this work BETA
Kevin Davey (2003). Is Mathematical Rigor Necessary in Physics? British Journal for the Philosophy of Science 54 (3):439-463.
James Ax (1978). The Elementary Foundations of Spacetime. Foundations of Physics 8 (7-8):507-546.

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Laurenz Hudetz (2015). Linear Structures, Causal Sets and Topology. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 52:294-308.

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