On Tarski's foundations of the geometry of solids (Q2893282)

In [``Les fondements de la géométrie des corps'', Księga Pamiątkowa I Zjazdu Matematyków 1929, 29--33 (1929)] \textit{A. Tarski} wrote an uncharacteristically vague note on the possibility of axiomatizing solid Euclidean geometry in terms of `spheres' and `being part of'. The authors present the contents of the paper, Tarski's general view of axiomatics, the reason why the paper does ``not live up to his own methodological ideals'', the reasons why ``Leśniewski's philosophy and systems do not play the significant role that one may be tempted to assign to them at first glance'' (Leśniewski having originated the analysis of the part-whole relation under the name of mereology). By analyzing the possible meanings of the domain of discourse, the authors find an interpretation under which Tarski's system does not need to be seen as having made the mistake ascribed to it by \textit{R. Gruszczyński} and \textit{A. Pietruszczak} [Bull. Symb. Log. 14, No. 4, 481--540 (2008; Zbl 1156.03011)].