Model theory with applications to algebra and analysis
By Zoé Chatzidakis, Dugald Macpherson, Anand Pillay, Alex Wilkie. 2008
320 citations recorded by the source corpus.
Subfields: Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/1b91560960693795ea1df32893cafcbdccfeeb62
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Theory and Mathematics
- Ehud Hrushovski
- Anand Pillay
- David Sherman
- Ilijas Farah
- Jonathan Pila
- R. Pink
- Michael Larsen
- Bradd Hart
In Geometry and Topology
- Ehud Hrushovski
- Jonathan Pila
- Anand Pillay
- Bradd Hart
- David Sherman
- Ronnie Nagloo
- F. Pop
- Ilijas Farah
Citations in the corpus
- Henselian implies large (2010, background): “article Harbater [Ha1], study torsors of finite groups Moret-Bailly [MB], study rationally connected varieties Kollár [Ko], study the elementary theory of function fields Poonen– Pop [P–P], etc.”
- Stable group theory and approximate subgroups (2009, methodology): “Our main tool is a cardinality estimate due in its original form to Larsen and Pink; in [21] it was presented as a dimension comparison lemma and slightly generalized in a number of directions; one of these will be needed here.”
- Finite subgroups of algebraic groups (2011, background): “In particular, Ehud Hrushovski and Frank Wagner [16] have reproved the basic “nonconcentration estimate” (Theorem 4.”
- On algebraic relations between solutions of a generic Painleve equation (2011, background): “Thanks also to Frank Nijhoff and Davide Penazzi for numerous discussions related to the material presented here.”
- On central extensions and definably compact groups in o-minimal structures (2008, unknown): “We also have, for h̄1 ∈ K2m, h̄2 ∈ K2n, Fm,K(h̄1) · Fn,K(h̄2) = Fm+n,K(h̄1, h̄2), and if for h̄ = (x1, y1, . . . , xn, yn) we let inv(h̄) = (yn, xn, yn−1, xn−1, . . . , y1, x1) then Fn,K(h̄) −1 = Fn,K(inv(h̄)).”
- Model theory of operator algebras III: elementary equivalence and II1 factors (2011, background): “Another important logical relation is finite representability, which induces a partial ordering based on the condition that one object embeds in an ultrapower of another.”
- O-minimality and the André-Oort conjecture for $\mathbb{C}^{n}$ (2011, background): “Thus if ΦN (x, y) = 0 and x is special, then y is also special.”