 The basic idea is simple: a theory TR reduces to a theory TB if and only if TR is derivable from TB with the possible help of the relevant bridge laws (here labeled ‘coordinating definitions’), often with an emphasis of the derivation of the laws of the reduced theory. If we add the remarks Nagel opened his discussion on reduction with—namely, that reduction has to be understood as a certain kind of explanation (1961: 338)—the core idea of the Nagel model is fully characterized. Adding Nagel’s idea of reduction as a kind of explanation, the so called “Nagel model of reduction” can be fully specified as follows: Reduction is (i) a kind of explanation relation, which (ii) holds between two theories iff (iii) one of these theories is derivable from the other, (iv) with the help of bridge laws under some conditions. The basic model covers two sorts of reduction, one in which bridge laws are not required (homogeneous cases) and one in which they are (nonhomogeneous cases; for a presentation of homogeneous cases of reductions and the question of whether or not alleged cases of reductions really should count as reductions in the Nagelian sense, see the entry on  intertheory relations in physics).  Nagel conceives of sciences or theories as developing entities that undergo changes, across which their vocabulary remains unchanged (though it is, presumably, sometimes extended). These successive states of theories are covered by the notion of homogeneous reductions—deduction of an early stage from a later stage of a theory is possible without bridge laws since they share a common vocabulary. Nonhomogeneous cases of reduction hold between pairs of different theories, employing different vocabularies. Whereas the former variant of reduction did not attract much attention (by Nagel and others), the latter has been a subject of intense discussion since Nagel introduced it in 1949.