6 citations · 14 across the 12 of their papers we have counts for
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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.
Cell decomposition and p-adic integration
Raf Cluckers
A semialgebraic bijection from the field of p-adic numbers to itself minus one point is constructed. Semialgebraic p-adic sets are classified up to semialgebraic bijection. A cell…
Grothendieck rings of Laurent series fields
Raf Cluckers
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…
Presburger sets and p-minimal fields
Raf Cluckers
We prove a cell decomposition theorem for Presburger sets and introduce a dimension theory for Z-groups with the Presburger structure. Using the cell decomposition theorem we obtai…