6 citations · 11 across the 3 of their papers we have counts for
7 papers · 1 filter
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…
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…
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…
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…