Lowness For Isomorphism And Degrees Of Genericity

A Turing degree d is said to be low for isomorphism if whenever two computable structures are d-computably isomorphic, then they are actually computably isomorphic. We construct a real that is 1-generic and low for isomorphism but not computable from a 2-generic and thus provide a counterexample to Franklin and Solomon's conjecture that the properly 1-generic degrees are neither low for isomorphism nor degrees of categoricity.