  We study Grothendieck rings (in the sense of logic) of fields. We prove the
triviality of the Grothendieck rings of certain fields by constructing
definable bijections which imply the triviality. More precisely, we consider
valued fields, for example, fields of Laurent series over the real numbers,
over p-adic numbers and over finite fields, and construct definable bijections
from the line to the line minus one point.
