2 citations · 3 across the 3 of their papers we have counts for
5 papers
On the strong separation conjecture
F Lucas, D. Schaub, M. Spivakovsky
This paper contains a partial result on the Pierce--Birkhoff conjecture on piece-wise polynomial functions defined by a finite collection {f 1,. .., f r} of polynomials. In the nin…
c-Regular cyclically ordered groups
Gérard Leloup, Francois Lucas
We define and we characterize regular and c-regular cyclically ordered abelian groups. We prove that every dense c-regular cyclically ordered abelian group is elementarily equivale…
First order theory of cyclically ordered groups
Michèle Giraudet, Gérard Leloup, Francois Lucas
By a result known as Rieger's theorem (1956), there is a one-to-one correspondence, assigning to each cyclically ordered group a pair where is a totally ordered gro…
Approximate roots of a valuation and the Pierce-Birkhoff Conjecture
François Lucas, James Madden, Daniel Schaub +1
This paper is a step in our program for proving the Piece-Birkhoff Conjecture for regular rings of any dimension (this would contain, in particular, the classical Pierce-Birkhoff c…
A connectedness theorem for real spectra of polynomial rings
François Lucas, James Madden, Daniel Schaub +1
Let R be a real closed field. The Pierce-Birkhoff conjecture says that any piecewise polynomial function f on R^n can be obtained from the polynomial ring R[x_1,...,x_n] by iterati…