The definition of special terms belongs in your Written Description. Then your Claims (which aren’t required for a provisional patent by the way) will be interpreted in view of the definitions in the description, as long as those definitions are clear to a PHOSITA (“person having ordinary skill in the art”).
If you litigate, there will be a claims construction phase. The only way I could imagine your custom definitions will not hold up is if they are contradictory or unclear, such that a PHOSITA would not understand them.
This will suffice internationally.
UPDATE: If you do define your own terms, or even if you use standard terms with some nuance, explicit definitions will be valuable to you in the event of infringement or invalidity litigation. You will save legal expense and increase the chance of a successful outcome in a Markman hearing (the courtroom proceeding that settles claim constructions). Explicit definitions will make it much harder for the opposing side to construe claim terms in a different way that may harm your position.
Disclaimer: I am not a lawyer.