• Publications
  • Influence
Tame structures and open cores
We study various notions of "tameness" for definably complete expansions of ordered fields. We mainly study structures with locally o-minimal open core, d-minimal structures, and dense pairs ofExpand
  • 12
  • 3
  • PDF
Definably complete Baire structures
We consider definably complete Baire expansions of ordered fields: every definable subset of the domain of the structure has a supremum and the domain cannot be written as the union of a definableExpand
  • 16
  • 2
Integration on surreal numbers
TLDR
A general scheme of definition for functions on No, generalising those for sum, product and exponential. Expand
  • 15
  • 2
  • PDF
Dimensions, matroids, and dense pairs of first-order structures
  • A. Fornasiero
  • Mathematics, Computer Science
  • Ann. Pure Appl. Log.
  • 24 July 2009
TLDR
A structure M is pregeometric if the algebraic closure is a pregeometry in all structures elementarily equivalent to M. We show that there is a corresponding abstract notion of density in models of T . Expand
  • 14
  • 1
  • PDF
Groups and rings definable in d-minimal structures
We study groups and rings definable in d-minimal expansions of ordered fields. We generalize to such objects some known results from o-minimality. In particular, we prove that we can endow aExpand
  • 6
  • 1
  • PDF
Embedding Henselian fields into power series
Abstract Every Henselian field of residue characteristic 0 admits a truncation-closed embedding in a field of generalised power series (possibly, with a factor set). As corollaries we obtain theExpand
  • 18
  • 1
  • PDF
O-Minimal Cohomology: Finiteness and invariance Results
TLDR
The topology of definable sets in an o-minimal expansion of a group is not fully understood due to the lack of a triangulation theorem. Expand
  • 12
  • 1
  • PDF
Algebraic entropy for amenable semigroup actions
We introduce two notions of algebraic entropy for actions of cancellative right amenable semigroups $S$ on discrete abelian groups $A$ by endomorphisms; these extend the classical algebraic entropyExpand
  • 8
  • 1
  • PDF
A FUNDAMENTAL DICHOTOMY FOR DEFINABLY COMPLETE EXPANSIONS OF ORDERED FIELDS
TLDR
An expansion of a definably complete field either defines a discrete subring, or the image of every definable discrete set is nowhere dense. Expand
  • 6
  • 1
  • PDF
Locally o-minimal structures and structures with locally o-minimal open core
  • A. Fornasiero
  • Mathematics, Computer Science
  • Ann. Pure Appl. Log.
  • 1 March 2013
TLDR
We study first-order expansions of ordered fields that are definably complete, and moreover either are locally o-minimal, or have a locally o -minimal open core. Expand
  • 14
...
1
2
3
4
...