Grothendieck rings of \mathbb{Z}-valued fields

Details Grothendieck rings of \mathbb{Z}-valued fields Grothendieck rings of \mathbb{Z}-valued fields

2003-11-25

arxiv.org/abs/math/0311435v1

Bull. Symbolic Logic 7 (2001), 262--269

Mathematics

Logic

8 pages

Scientific paper

We 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.

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