2 citations · 2 across the 4 of their papers we have counts for
6 papers
Finding suitably generic points on curves with an application to the construction of rigid real closed fields
Dragos Ghioca, David Marker, Charles Steinhorn
Let be an algebraically closed field of characteristic 0 and transcendence degree at least 2. Let be an irreducible curve defined over but not defined over t…
Multidimensional asymptotic classes
Sylvy Anscombe, Dugald Macpherson, Charles Steinhorn +1
We develop a general framework (multidimensional asymptotic classes, or m.a.c.s) for handling classes of finite first order structures with a strong uniformity condition on cardina…
Rigid Real Closed Fields
David Marker, Charles Steinhorn
We construct a non-Archimedean real closed field of transcendence degree two with no non-trivial automorphisms
Pseudofinite structures and simplicity
Dario Garcia, Dugald Macpherson, Charles Steinhorn
We explore a notion of pseudofinite dimension, introduced by Hrushovski and Wagner, on an infinite ultraproduct of finite structures. Certain conditions on pseudofinite dimension a…
Decomposable ordered groups
Eliana Barriga, Alf Onshuus, Charles Steinhorn
Decomposable ordered structures were introduced in \cite{OnSt} to develop a general framework to study `finite-dimensional' totally ordered structures. This paper continues this wo…
Uncountable Real Closed Fields with PA Integer Parts
David Marker, James Schmerl, Charles Steinhorn
D'Aquino, Knight and Starchenko classified the countable real closed fields with integer parts that are nonstandard models of Peano Arithmetic. We rule out some possibilities for e…