It is proved that every computable locally finite structure with finitely many functions has a presentation computable in polynomial time. Furthermore, a structure computable in polynomial time is polynomially categorical… Click to show full abstract
It is proved that every computable locally finite structure with finitely many functions has a presentation computable in polynomial time. Furthermore, a structure computable in polynomial time is polynomially categorical iff it is finite. If a structure is computable in polynomial time and locally finite then it is weakly polynomially categorical (i.e., categorical with respect to primitive recursive isomorphisms) iff it is finite.
               
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