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On generalizing the logic-approach to space-time towards general relativity: first steps

In Vincent F. Hendricks (ed.), First-Order Logic Revisited. Logos. pp. 225--268 (2004)

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  1. A Formal Construction of the Spacetime Manifold.Thomas Benda - 2008 - Journal of Philosophical Logic 37 (5):441 - 478.
    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 (...)
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  • 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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