Independent Axioms for Minkowski Space-Time (Chapman & Hall/CRC Research Notes in Mathematics Series)

The primary aim of this monograph is to clarify the undefined primitive concepts and the axioms which form the basis of Einstein's theory of special relativity. Minkowski space-time is developed from a set of independent axioms, stated in terms of a single relation of betweenness. It is shown that all models are isomorphic to the usual coordinate model, and the axioms are consistent relative to the reals. 1. Introduction -- 2. Primitive Notions And Axioms -- 3. Temporal Order On A Path -- 4. Collinearity And Temporal Order -- 5. Existence And Properties Of Collinear Sets -- 6. Paths And Optical Lines In A Collinear Set -- 7. Theory Of Parallels -- 8. One-dimensional Kinematics -- 9. Three-dimensional Theorems -- 10. Standard Model Of Minkowski Space-time -- 11. Independence Models -- App. 1. Veblen's Axioms For An Ordered Geometry -- App. 2. Alternative Axiom Systems -- App. 3. Open Questions. John W. Schutz. Includes Bibliographical References (p. 233-239) And Index. The main purpose of describing a theory axiomatically is to clarify the basic concepts of the theory and the assumptions on which it is based.