# turing machines – A question for mapping reductions

Given a language $$A$$ How can you construct a language? $$B$$ so that $$A leq_m B$$ but $$B not leq_m A$$?

I know that when we leave $$B = { langle M, w rangle : | : M text {is an Oracle Turing machine for} A text {and} M text {accepted} w }$$, then $$A leq_T B$$ but $$B not leq_T A$$But is there a simple construction for mapping reductions that does not involve oracles?