  Interdefinability of timelike, lightlike and spacelike relatedness of
Minkowski spacetime is investigated in detail in the paper, with the aim of
finding the simplest definitions. Based on ideas scattered in the literature,
definitions are given between any two of these relations that use only 4
variables. All these definitions work over arbitrary Euclidean fields in place
of the field of reals, if the dimension n of spacetime is greater than two. If
n=2, the definitions work over arbitrary ordered fields except the ones based
on lightlike relatedness (where no definition can work by symmetry). None of
these relations can be defined from another one using only 3 variables. Our
four-variable definitions use only one universal and one existential
quantifiers in a specific order. In some of the cases, we show that the order
of these quantifiers can be reversed for the price of using twice as many
quantifiers. Except two cases, we provide existential/universal definitions
using 5 variables or show that no existential/universal definition exists.
There are no existential/universal definitions between any two of these
relations using only 4 variables. It remains open whether there is an
existential (universal) definition of timelike (lightlike) relatedness from
spacelike relatedness if $n>2$. Finally, several other open problems related to
the quantifier complexity of the simplest possible definitions are given.

Logic