11 citations · 18 across the 9 of their papers we have counts for
9 papers · 1 filter
Monotone -convex -differential fields
Elliot Kaplan, Nigel Pynn-Coates
Let be a complete, model complete o-minimal theory extending the theory of real closed ordered fields and assume that is power bounded. Let be a model of equipped w…
Liouville closed -fields
Elliot Kaplan
Let be an o-minimal theory extending the theory of real closed ordered fields. An -field is a model of equipped with a -derivation such that the underlying orde…
-convex -differential fields and their immediate extensions
Elliot Kaplan
Let be a polynomially bounded o-minimal theory extending the theory of real closed ordered fields. Let be a model of equipped with a -convex valuation ring and a …
Model completeness for the differential field of transseries with exponentiation
Elliot Kaplan
We show that the expansion of the valued differential field of logarithmic-exponential transseries by its natural exponential function is model complete. We give an axiomatization…
Surreal ordered exponential fields
Philip Ehrlich, Elliot Kaplan
In [26], the algebraico-tree-theoretic simplicity hierarchical structure of J. H. Conway's ordered field of surreal numbers was brought to the fore and employed to pr…
Generic derivations on o-minimal structures
Antongiulio Fornasiero, Elliot Kaplan
Let be a complete, model complete o-minimal theory extending the theory RCF of real closed ordered fields in some appropriate language . We study derivations on models $…
Logarithmic Hyperseries
Lou van den Dries, Joris van der Hoeven, Elliot Kaplan
We define the field of logarithmic hyperseries, construct on natural operations of differentiation, integration, and composition, establish the basic prop…
Pairs of Theories Satisfying a Mordell-Lang Condition
Alexi Block Gorman, Philipp Hieronymi, Elliot Kaplan
This paper proposes a new setup for studying pairs of structures. This new framework includes many of the previously studied classes of pairs, such as dense pairs of o-minimal stru…
Number Systems with Simplicity Hierarchies II
Philip Ehrlich, Elliot Kaplan
In [15], the algebraico-tree-theoretic simplicity hierarchical structure of J. H. Conway's ordered field No of surreal numbers was brought to the fore and employed to provide neces…