11 citations · 49 across the 21 of their papers we have counts for
30 papers · 1 filter
Uniform Bounds in D-Minimal Structures
Madie Farris, Philipp Hieronymi
Let be an expansion of the real field such that every subset of definable in either has interior or is a finite union of discrete sets. Ans…
Axiomatizations of Presburger Arithmetic With Predicates For Powers
Philipp Hieronymi, Michael Reitmeir, Xiaoduo Wang
We give a complete first-order axiomatization of the structure , where is a set of pairwise multipl…
Decidability bounds for Presburger arithmetic extended by sine
Eion Blanchard, Philipp Hieronymi
We consider Presburger arithmetic extended by the sine function, call this extension sine-Presburger arithmetic (-PA), and systematically study decision problems for sets of…
A strong version of Cobham's theorem
Philipp Hieronymi, Chris Schulz
Let be two multiplicatively independent integers. Cobham's famous theorem states that a set is both -recognizable and -recognizable…
Pathological examples of structures with o-minimal open core
Alexi Block Gorman, Erin Caulfield, Philipp Hieronymi
This paper answers several open questions around structures with o-minimal open core. We construct an expansion of an o-minimal structure by a unary predicate such th…
Fractals and the monadic second order theory of one successor
Philipp Hieronymi, Erik Walsberg
We show that if is virtually any classical fractal subset of , then interprets the monadic second-order theory of . This res…
Expansions of the real field by discrete subgroups of Gl
Philipp Hieronymi, Erik Walsberg, Samantha Xu
Let be an infinite discrete subgroup of Gl. Then either is interdefinable with for some…
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…
Presburger Arithmetic with algebraic scalar multiplications
Philipp Hieronymi, Danny Nguyen, Igor Pak
We consider Presburger arithmetic (PA) extended by scalar multiplication by an algebraic irrational number , and call this extension -Presburger arithmetic (-PA). We show…
A tetrachotomy for expansions of the real ordered additive group
Philipp Hieronymi, Erik Walsberg
Let be an expansion of the ordered real additive group. When is o-minimal, it is known that either defines an ordered field isomorphic to…
The Choice Property in tame expansions of o-minimal structures
Pantelis E. Eleftheriou, Ayhan Günaydın, Philipp Hieronymi
We establish the choice property, a weak analogue of definable choice, for certain tame expansions of o-minimal structures. Most noteworthily, dense pairs of real closed fields hav…
Wild theories with o-minimal open core
Philipp Hieronymi, Travis Nell, Erik Walsberg
Let be a consistent o-minimal theory extending the theory of densely ordered groups and let be a consistent theory. Then there is a complete theory extending suc…
Definability and decidability in expansions by generalized Cantor sets
William Balderrama, Philipp Hieronymi
We determine the sets definable in expansions of the ordered real additive group by generalized Cantor sets. Given a natural number , we say a set is a generalized Can…
How to avoid a compact set
Antongiulio Fornasiero, Philipp Hieronymi, Erik Walsberg
A first-order expansion of the -vector space structure on does not define every compact subset of every if and only if topological and Hausd…
Interpreting the monadic second order theory of one successor in expansions of the real line
Philipp Hieronymi, Erik Walsberg
We give sufficient conditions for a first order expansion of the real line to define the standard model of the monadic second order theory of one successor. Such an expansion does…
Distal and Non-Distal Pairs
Philipp Hieronymi, Travis Nell
The aim of this note is to determine whether certain non-o-minimal expansions of o-minimal theories which are known to be NIP, are also distal. We observe that while tame pairs of…
Structure theorems in tame expansions of o-minimal structures by a dense set
Pantelis E. Eleftheriou, Ayhan Günaydin, Philipp Hieronymi
We study sets and groups definable in tame expansions of o-minimal structures. Let be an expansion of an o-minimal $\mathcal…
Metric dimensions and tameness in expansions of the real field
Philipp Hieronymi, Chris Miller
For first-order expansions of the field of real numbers, nondefinability of the set of natural numbers is equivalent to equality of topological and Assouad dimension on images of c…
A tame Cantor set
Philipp Hieronymi
A Cantor set is a non-empty, compact set that has neither interior nor isolated points. In this paper a Cantor set is constructed such that every set defina…
When is scalar multiplication decidable?
Philipp Hieronymi
Let be a subfield of . The theory of viewed as an ordered -vector space and expanded by a predicate for is decidable if and only if …
Expansions of the ordered additive group of real numbers by two discrete subgroups
Philipp Hieronymi
The theory of is decidable if is quadratic. If is the golden ratio, defines multiplica…
Ostrowski numeration systems, addition and finite automata
Philipp Hieronymi, Alonza Terry
We present an elementary three pass algorithm for computing addition in Ostrowski numeration systems. When is quadratic, addition in the Ostrowski numeration system based on $a…
A fundamental dichotomy for definably complete expansions of ordered fields
Antongiulio Fornasiero, Philipp Hieronymi
An expansion of a definably complete field either defines a discrete subring, or the image of a definable discrete set under a definable map is nowhere dense. As an application we…
Interpreting the projective hierarchy in expansions of the real line
Philipp Hieronymi, Michael Tychonievich
We give a criterion when an expansion of the ordered set of real numbers defines the image of the expansion of the real field by the set of natural numbers under a semialgebraic in…