The definition of pH is:

pH = -log 10[H^+]

what is the defintion of the [OH^-]...
is it pOH = -log 10[OH^-]?

Yes!!

pH = - log10 anything.
pKa = -log Ka
Pkb = -log Kb
pKw = -log Kw = 14
PKsp = -log Ksp (solubility product)
and so on into the night.

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