[Tennenbaum's theorem](http://www.logicmatters.net/resources/pdfs/TennenbaumTheorem.pdf) does not apply to [Robinson Arithmetic ($Q$)](https://en.wikipedia.org/wiki/Robinson_arithmetic#Metamathematics). 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](https://en.wikipedia.org/wiki/Peano_axioms#First-order_theory_of_arithmetic) 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](https://en.wikipedia.org/wiki/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?