An axiomatic foundation of relativistic spacetime

Thomas Benda

pp. 2009-2024

in: Gergely Szekely (ed), Logic and relativity theory, Synthese 192 (7), 2015.

Abstract

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.