Tennenbaum's theorem does not apply to Robinson Arithmetic ($Q$). There is a computable, nonstandard model of $Q$ "consisting of integer-coefficient polynomials with positive leading coefficient, plus the zero polynomial, with their usual arithmetic."
What is an example of how the first order induction schema fails in a computable, nonstandard model of $Q$? Can such a model have a predicate, in the language of Q, that is only true for standard natural numbers and false for "infinite" natural numbers? Can a computable nonstandard model have overspill?
Given the model above, what is an example of a statement, in the language of $Q$, that is true for the zero polynomial and all successors of the zero polynomial and false for some other polynomial in the model?