In the Footsteps of Hilbert: The Andréka-Németi Group’s Logical Foundations of Theories in Physics

Investigations of isotropy and homogeneity of spacetime in first-order logic

“…It is not difficult to see that there are linear proper orthochronous Poincaré transformations f 1 , f 2 and f 3 taking the time unit vector e 1 , respectively, to p 1 := (5/3, 4/3, 0, 0), p 2 := (5/3, 0, 4/3, 0) and p 3 := (5/3, 0, 0, 4/3). 12 By Poi ↑ + ⊆ W o , we can choose o 1 , o 2 , o 3 such that w oo 1 = f 1 , w oo 2 = f 2 and w oo 3 = f 3 . By definition of worldline, for the choice of o 1 , o 2 , o 3 and p 1 , p 2 , p 3 above, (2)h o l d s .…”

“…For discussion of the methodological and epistemological significance of this project, see Friend and Molinini [13,14]. For a comprehensive comparison between Hilbert's project on the foundations of physics and the Andréka-Németi project, see Formica and Friend [12].…”