LAUSR

We present an elementary system of axioms for the geometry of Minkowski spacetime. It strikes a balance between a simple and streamlined set of axioms and the attempt to give a direct formalization in first-order logic of the standard account of Minkowski spacetime in Maudlin ( 2012 ) and Malament ( unpublished ). It is intended for future use in the formalization of physical theories in Minkowski spacetime. The choice of primitives is in the spirit of Tarski ( 1959 ): a predicate of betwenness and a four place predicate to compare the square of the relativistic intervals. Minkowski spacetime is described as a four dimensional ‘vector space’ that can be decomposed everywhere into a spacelike hyperplane—which obeys the Euclidean axioms in Tarski and Givant ( The Bulletin of Symbolic Logic , 5 (2), 175–214 1999 )—and an orthogonal timelike line. The length of other ‘vectors’ are calculated according to Pythagoras’ theorem. We conclude with a Representation Theorem relating models M $\mathfrak {M}$ of our system M 1 ${\mathscr{M}}^{1}$ that satisfy second order continuity to the mathematical structure 〈 ℝ 4 , η a b 〉 $\langle \mathbb {R}^{4}, \eta _{ab}\rangle $ , called ‘Minkowski spacetime’ in physics textbooks.