E. Kaplan

activity

20142023

most citedGeneric derivations on o-minimal structures

11 citations · 18 across the 9 of their papers we have counts for

collaborators

12 papers

math.LO2023

Monotone $T$ -convex $T$ -differential fields

Elliot Kaplan, Nigel Pynn-Coates

Let $T$ be a complete, model complete o-minimal theory extending the theory of real closed ordered fields and assume that $T$ is power bounded. Let $K$ be a model of $T$ equipped w…

math.CO2022

Hilbert polynomials for finitary matroids

Antongiulio Fornasiero, Elliot Kaplan

We consider a tuple $Φ = (ϕ_{1}, \dots, ϕ_{m})$ of commuting maps on a finitary matroid $X$ . We show that if $Φ$ satisfies certain conditions, then for any finite set $A \subseteq X$ , the…

math.LO2022

Liouville closed $H_{T}$ -fields

Elliot Kaplan

Let $T$ be an o-minimal theory extending the theory of real closed ordered fields. An $H_{T}$ -field is a model $K$ of $T$ equipped with a $T$ -derivation such that the underlying orde…

math.LO2021★ 3 cited

$T$ -convex $T$ -differential fields and their immediate extensions

Elliot Kaplan

Let $T$ be a polynomially bounded o-minimal theory extending the theory of real closed ordered fields. Let $K$ be a model of $T$ equipped with a $T$ -convex valuation ring and a $T$ …

math.LO2020★ 1 cited

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…

math.LO2020

Surreal ordered exponential fields

Philip Ehrlich, Elliot Kaplan

In [26], 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 pr…

Monotone T-convex T-differential fields

Hilbert polynomials for finitary matroids

Liouville closed HT​-fields

T-convex T-differential fields and their immediate extensions

Model completeness for the differential field of transseries with exponentiation

Surreal ordered exponential fields

Monotone $T$ -convex $T$ -differential fields

Liouville closed $H_{T}$ -fields

$T$ -convex $T$ -differential fields and their immediate extensions