6 citations · 14 across the 12 of their papers we have counts for
11 papers
Analytic cell decomposition and analytic motivic integration
R. Cluckers, L. Lipshitz, Z. Robinson
The main results of this paper are a Cell Decomposition Theorem for Henselian valued fields with analytic structure in an analytic Denef-Pas language, and its application to analyt…
Ax-Kochen-Er{š}ov Theorems for -adic integrals and motivic integration
R. Cluckers, F. Loeser
This survey paper, to appear in he proceedings of the Miami Winter School ``Geometric Methods in Algebra and Number Theory'', is concerned with extending classical results à la Ax-…
The Fundamental Theorem of prehomogeneous vector spaces modulo . With an appendix "L-functions of prehomogeneous vector spaces" by Fumihiro Sato
Raf Cluckers, Adriaan Herremans
For a number field with ring of integers , we prove an analogue over finite rings of the form of the Fundamental Theorem on the…
Grothendieck rings of \mathbb{Z}-valued fields
Raf Cluckers, Deirdre Haskell
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 p…
Classification of semi-algebraic -adic sets up to semi-algebraic bijection
Raf Cluckers
We prove that two infinite p-adic semi-algebraic sets are isomorphic (i.e. there exists a semi-algebraic bijection between them) if and only if they have the same dimension.
Model theory of valued fields
Raf Cluckers
We give a proposal for future development of the model theory of valued fields. We also summarize some recent results on p-adic numbers.