3 citations · 8 across the 13 of their papers we have counts for
23 papers
On the global linear Zarankiewicz problem
Pantelis E. Eleftheriou, Aris Papadopoulos
The `global' Zarankiewicz problem for hypergraphs asks for an upper bound on the number of edges of a finite -hypergraph in terms of the number of its vertices, assumi…
Orthogonality and domination in o-minimal expansions of ordered groups
Pablo Andújar Guerrero, Pantelis E. Eleftheriou, Rosario Mennuni
We analyse domination between invariant types in o-minimal expansions of ordered groups, showing that the domination poset decomposes as the direct product of two posets: the domin…
Exact VC-Dimensions of Certain Geometric Set Systems
Pantelis E. Eleftheriou, Aris Papadopoulos, Francis Westhead
The VC-dimension of a family of sets is a measure of its combinatorial complexity used in machine learning theory, computational geometry, and even model theory. Computing the VC-d…
Orthogonal decomposition of definable groups
Alessandro Berarducci, Pantelis E. Eleftheriou, Marcello Mamino
Orthogonality in model theory captures the idea of absence of non-trivial interactions between definable sets. We introduce a somewhat opposite notion of cohesiveness, capturing th…
Groups definable in weakly o-minimal non-valuational structures
Pantelis E. Eleftheriou
Let be a weakly o-minimal non-valuational structure, and its canonical o-minimal extension (by Wencel). We prove that every group definable in $\mathc…
On semibounded expansions of ordered groups
Pantelis E. Eleftheriou, Alex Savatovsky
We explore "semibounded" expansions of arbitrary ordered groups; namely, expansions that do not define a field on the whole universe. We show that if $\mathcal R=\langle R, <, +, \…
Coincidence of dimensions in closed ordered differential fields
Pantelis E. Eleftheriou, Omar Leon Sanchez, Nathalie Regnault
Let be a closed ordered differential field, in the sense of M. Singer, and its field of constants. In this note, we prove that, for set…
Expansions of real closed fields which introduce no new smooth functions
Pantelis E. Eleftheriou, Alex Savatovsky
We prove the following theorem: let be an expansion of the real field , such that every definable set (I) is a uniform countable unio…
Small sets in Mann pairs
Pantelis E. Eleftheriou
Let be an expansion of a real closed field by a dense subgroup of with the Man…
Locally definable subgroups of semialgebraic groups
Elías Baro, Pantelis E. Eleftheriou, Ya'acov Peterzil
We prove the following instance of a conjecture stated in arXiv:1103.4770. Let be an abelian semialgebraic group over a real closed field and let be a semialgebraic sub…
Strongly minimal groups in o-minimal structures
Pantelis Eleftheriou, Assaf Hasson, Ya'acov Peterzil
We prove Zilber's Trichotomy Conjecture for strongly minimal expansions of two-dimensional groups, definable in o-minimal structures: Theorem. Let M be an o-minimal expansion of a…
Characterizing o-minimal groups in tame expansions of o-minimal structures
Pantelis E. Eleftheriou
We establish the first global results for groups definable in tame expansions of o-minimal structures. Let be an expansion of an o-minimal structure that…
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…
Product cones in dense pairs
Pantelis E. Eleftheriou
Let be an o-minimal expansion of an ordered group, and a dense set such that certain tameness conditions hold. We introduc…
Counting algebraic points in expansions of o-minimal structures by a dense set
Pantelis E. Eleftheriou
The Pila-Wilkie theorem states that if a set is definable in an o-minimal structure and contains `many' rational points, then it contains an i…
Small sets in dense pairs
Pantelis E. Eleftheriou
Let be an expansion of an o-minimal structure by a dense set , such that three tameness conditions…
Semi-linear stars are contractible
Pantelis E. Eleftheriou
Let be an ordered vector space over an ordered division ring. We prove that every definable set is a finite union of relatively open definable subsets which are defina…
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…
On definable Skolem functions in weakly o-minimal non-valuational structures
Pantelis E. Eleftheriou, Assaf Hasson, Gil Keren
We prove that all known examples of weakly o-minimal non-valuational structures have no definable Skolem functions. We show, however, that such structures eliminate imaginaries up…
Coverings by open cells
Mário J. Edmundo, Pantelis Eleftheriou, Luca Prelli
We prove that in a semi-bounded o-minimal expansion of an ordered group every non-empty open definable set is a finite union of open cells.
Definable groups as homomorphic images of semilinear and field-definable groups
Pantelis Eleftheriou, Ya'acov Peterzil
We analyze definably compact groups in o-minimal expansions of ordered groups as a combination of semi-linear groups and groups definable in o-minimal expansions of real closed fie…
Interpretable groups are definable
Janak Ramakrishnan, Ya'acov Peterzil, Pantelis Eleftheriou
We prove that in an arbitrary o-minimal structure, every interpretable group is definably isomorphic to a definable one. We also prove that every definable group lives in a cartesi…
Definable quotients of locally definable groups
Pantelis Eleftheriou, Ya'acov Peterzil
We study locally definable abelian groups $\CU$ in various settings and examine conditions under which the quotient of $\CU$ by a discrete subgroup might be definable. This turns o…