Nonstandard polynomials: algebraic properties and elementary equivalence

Alexei Myasnikov, Andrey Nikolaev

We solve the first-order classification problem for rings $R$ of polynomials $F[x_1,\dots ,x_n]$ and Laurent polynomials $F[x_1,x_1^{-1},\dots ,x_n,x_n^{-1}]$ with coefficients i…