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Full Idea
We can distinguish Identifying Reductionism (as in 'persons are bodies'), or Constitutive Reductionism (as in 'persons are distinct, but consist of thoughts etc.'), or Eliminative Reductionism (as in 'there are no persons, only thoughts etc.').
Gist of Idea
Reduction can be by identity, or constitution, or elimination
Source
report of Derek Parfit (The Unimportance of Identity [1995], p.295) by PG - Db (ideas)
Book Ref
'Personal Identity', ed/tr. Martin,R /Barresi,J [Blackwells 2003], p.295
A Reaction
Constitutive Reductionism seems the most common one, as in 'chemistry just consists of lots of complicated physics'. He doesn't mention bridge laws, which are presumably only required in more complicated cases of constitutive reduction.