Minkowski Spacetime can be treated as either having the signature $(+,-,-,-)$ or more commonly $(+,+,+,-)$ as in Minkowski Spacetime the spacetime interval between two events is the quantity that is the same for all observers, and with $ct=w$, and $\Delta{s^2}$ giving the spacetime interval between two events $\Delta{s^2}=\Delta{x^2}+\Delta{y^2}+\Delta{z^2}-\Delta{w^2}$. There is also a Euclidean Signature with the signature $(+,+,+,+)$, in which the spacetime interval between any two events is just given by the euclidean distance formula $\Delta{s^2}=\Delta{x^2}+\Delta{y^2}+\Delta{z^2}+\Delta{w^2}$.

In a sense Galilean Spacetime is in between Minkowski and Euclidean Spacetime as in Minkowski Spacetime the spacetime path of a body accelerating at a constant rate is a hyperbole, in Euclidean Spacetime the spacetime path of an object with constant acceleration is a semi circle, and in Galilean Spacetime the path of an object accelerating at a constant rate is a parabola.

In Galilean Spacetime, if two events aren't simultaneous, then the time between the two events events is the same in all reference frames, but the spatial distance between two events is not the same in all reference frames, and the time between two events does not depend on their separation in the x, y, or z dimensions.

So can we label Galilean Spacetime as having the signature $(0,0,0,+)$?