A result of GrĂ¤del and McColm shows that over finite structures, the logic DTCL is strictly less expressive than the logic TCL. My question is: can this result be translated into some separation result concerning Turing machines with atoms?

A result of GrĂ¤del and McColm shows that over finite structures, the logic DTCL is strictly less expressive than the logic TCL. My question is: can this result be translated into some separation result concerning Turing machines with atoms?