Reading about Tarski's axioms of geometry https://en.wikipedia.org/wiki/Tarski%27s_axioms I was puzzeling how they would look for 3 dimensional geometry.
the big problem then is the upper dimension Axiom
For 2 dimensions it is (copied from wikipedia)
$(xu \equiv xv \land yu \equiv yv \land zu \equiv zv \land u \ne v) \rightarrow (Bxyz \lor Byzx \lor Bzxy)$
in 3 dimensional geometry it should be something like:
For every points P , Q , X, Y and Z if PX = QX, PY=QY and PZ= QZ then there is a plane A and X , Y and Z all belong to plane A .
But how to formulate plane A in Tarski's axioms?