Yes, It determines the kind of objection they don't have.
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AnonymousIs "in principle" a determiner in the noun phrase "no in principle objection"?No. It's a preposition phrase. It modifies the noun "objection". As such I can imagine some writers using a hyphen (in-principle). Compare: no material objection
CalifJimNo. It's a preposition phrase.Thank you for the explanation.