An axiomatic foundation of relativistic spacetime

• Autores: Thomas Benda
• Localización: Synthese, ISSN-e 1573-0964, Vol. 192, Nº. 7, 2015, págs. 2009-2024
• Idioma: inglés
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• Resumen

  • 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 urelemente. Sets generated from the empty set are mathematically interpreted, all other sets are physically interpreted