19 citations · 59 across the 19 of their papers we have counts for
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A class of fields with a restricted model completeness property
Philip Dittmann, Dion Leijnse
We introduce and study a natural class of fields in which certain first-order definable sets are existentially definable, and characterise this class by a number of equivalent cond…
Denseness results in the theory of algebraic fields
Sylvy Anscombe, Philip Dittmann, Arno Fehm
We study when the property that a field is dense in its real and p-adic closures is elementary in the language of rings and deduce that all models of the theory of algebraic fields…
The dimension growth conjecture, polynomial in the degree and without logarithmic factors
Wouter Castryck, Raf Cluckers, Philip Dittmann +1
We address Heath-Brown's and Serre's dimension growth conjecture (proved by Salberger), when the degree grows. Recall that Salberger's dimension growth results give bounds of t…
A p-adic analogue of Siegel's Theorem on sums of squares
Sylvy Anscombe, Philip Dittmann, Arno Fehm
Siegel proved that every totally positive element of a number field K is the sum of four squares, so in particular the Pythagoras number is uniformly bounded across number fields.…
Approximation theorems for spaces of localities
Sylvy Anscombe, Philip Dittmann, Arno Fehm
The classical Artin--Whaples approximation theorem allows to simultaneously approximate finitely many different elements of a field with respect to finitely many pairwise inequival…