Single-layer and multilayer imageable elements have a substrate and at least one imageable layer and can be used to prepare positive-working lithographic printing plates. The imageable elements also include a radiation absorbing compound and a solvent-resistant polymer binder comprising an —N(R)—C(═X)—N(R′)—S(═O)2— moiety that is attached to the polymer backbone, wherein X is O or S, R and R′ are independently hydrogen, halo, or an alkyl group having 1 to 6 carbon atoms. This solvent-resistant polymer binder is located in the imageable layer closest to the substrate and provides improved chemical resistance.