An axiomatic foundation of relativistic spacetime

Axiomatizations of the General Theory of Relativity.have occasionally been conducted to achieve precision and clarification of underlying concepts. Rigorous and inspiring work towards that aim based on first-order logic has been performed by Professor Németi and his working group (see references below). A complementary approach (Benda 2008) constructs the relativistic spacetime manifold ab initio in a theory ST, which is a conservative extension of Zermelo’s Z with urelemente, interpreted as worldlines. The present work contains a few modifications and continues towards the construction of a metric, from where the Einstein tensor is readily built.