Qualitative Theories of Space-Time

Abstract

This is an attempt to formulate (along the line of H. Field's nominalization program) purely qualitative versions of two theories of space time: Galilean and Minkowskian theories. The starting point is to present qualitative theory for affine geometry, which is based only on one primitive predicate: „between”. Then it is shown that with the help of this predicate whole mathematical structure of affine geometry can be reconstructed as a simple definitional extension. As a next step it is shown in details how the same procedure can be carried out for both theories mentioned above.