29 citations · 43 across the 29 of their papers we have counts for
12 papers · 1 filter
Automorphism Groups of Countable Stable Structures
Gianluca Paolini, Saharon Shelah
For every countable structure we construct an -stable countable structure such that and are topologically isomorphic. This shows that it is impo…
The Class of Countable Projective Planes is Borel Complete
Gianluca Paolini
We observe that Hall's free projective extension of partial planes is a Borel map, and use a modification of the construction introduced in [9] to conclude that th…
Polish Topologies for Graph Products of Groups
Gianluca Paolini, Saharon Shelah
We give strong necessary conditions on the admissibility of a Polish group topology for an arbitrary graph product of groups , and use them to give a characterization mo…
A New -Stable Plane
Gianluca Paolini
We use a variation on Mason's -function as a pre-dimension function to construct a not one-based -stable plane (i.e. a simple rank matroid) which does not admit an al…
A Universal Homogeneous Simple Matroid of Rank
Gianluca Paolini
We construct a -homogeneous universal simple matroid of rank , i.e. a countable simple rank~ matroid which -embeds every finite simple rank matroid,…
The Class of Non-Desarguesian Projective Planes is Borel Complete
Gianluca Paolini
For every infinite graph we construct a non-Desarguesian projective plane of the same size as such that and iff $P^*_{Γ_1}…
Group Metrics for Graph Products of Cyclic Groups
Gianluca Paolini, Saharon Shelah
We complement the characterization of the graph products of cyclic groups admitting a Polish group topology of [9] with the following result. Let $G = G(Γ, \ma…
Polish Topologies for Graph Products of Cyclic Groups
Gianluca Paolini, Saharon Shelah
We give a complete characterization of the graph products of cyclic groups admitting a Polish group topology, and show that they are all realizable as the group of automorphisms of…
The Automorphism Group of Hall's Universal Group
Gianluca Paolini, Saharon Shelah
We study the automorphism group of Hall's universal locally finite group . We show that in every subgroup of index lies between the pointwise and the setwise st…
The Strong Small Index Property for Free Homogeneous Structures
Gianluca Paolini, Saharon Shelah
We show that in algebraically locally finite countable homogeneous structures with a free stationary independence relation the small index property implies the strong small index p…
Reconstructing Structures with the Strong Small Index Property up to Bi-Definability
Gianluca Paolini, Saharon Shelah
Let be the class of countable structures with the strong small index property and locally finite algebraicity, and the class of s…
No Uncountable Polish Group Can be a Right-Angled Artin Group
Gianluca Paolini, Saharon Shelah
We prove that no uncountable Polish group can admit a system of generators whose associated length function satisfies the following conditions: (i) if , then $lg(x) \leq…