2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69334We prove the triviality of the Grothendieck ring of a integer-valued field K under slight conditions on the logical language and on K. We construct a definable bijection from the plane K^2 to itself minus a point. When we specialize to local fields with finite residue field, we construct a definable bijection from the valuation ring to itself minus a point.8 pagesLogictext