2002/10/22 by Raf Cluckers
Mathematics · #math.LO #msc:03C60 #msc:12L12 #msc:03C07
published as J. Algebra 272 (2004), 692--700 · 9 pages
arxiv created 2002/10/22 · arxiv updated 2009/11/30
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.