A strict order satsifies:

antisymmetric /\ weak order.

commonly denoted with ">".

From a strict order you can build a weak order and equivalence as follows:
x~y <=> x!>y /\ y!>x

x=>y <=> y!>x

There is a theorem which states the above method works.

source

jl@crush.caltech.edu index

extension

choice

order