6 papers
-holomorphic functions with definable real part
Antonio Carbone, Enrico Savi
Let be a real closed field and its algebraic closure. Let be an open and definable set in a fixed o-minimal structure. In this note, we study the relat…
Algebraic realization of stable Poincaré-Reeb graphs
Enrico Savi
We introduce the notion of domain of finite type generalizing an earlier work of Bodin, Popescu-Pampu and Sorea. Then, we prove that every finite g…
On the first-order theories of quaternions and octonions
Enrico Savi
Let be the language of rings. We provide an axiomatization of the -theories of quaternions and octonions and characterize their models: they coincide, up to isomorphism, wit…
A relative Nash-Tognoli theorem over and application to the -algebraicity problem
Enrico Savi
We prove a relative version over of Nash-Tognoli theorem, that is: Let be a compact smooth manifold with closed smooth submanifolds in general p…
The Nash-Tognoli theorem over the rationals and its version for isolated singularities
Riccardo Ghiloni, Enrico Savi
Let be the field of rational numbers and let be a subset of . We say that is -algebraic if it is the common zero set in $\mathbb{R}^n…
On the degree of global smoothings for subanalytic sets
Enrico Savi
In [4] Bierstone and Parusinski proved the existence of global smoothings for closed subanalytic sets, both in an embedded and a non-embedded sense. In particular, in the non-embed…