5 papers
Strongly Minimal Steiner Systems I: Existence
John Baldwin, Gianluca Paolini
A linear space is a system of points and lines such that any two distinct points determine a unique line; a Steiner -system (for ) is a linear space such that each lin…
First-Order Model Theory of Free Projective Planes
Tapani Hyttinen, Gianluca Paolini
We prove that the theory of open projective planes is complete and strictly stable, and infer from this that Marshall Hall's free projective planes are al…
Some Results on Polish Groups
Gianluca Paolini, Saharon Shelah
We prove that no quantifier-free formula in the language of group theory can define the -half graph in a Polish group, thus generalising some results from [6]. We then po…
On a Cardinal Invariant Related to the Haar Measure Problem
Gianluca Paolini, Saharon Shelah
In [6], given a metrizable profinite group , a cardinal invariant of the continuum was introduced, and a positive solution to the Haar Measure Problem for …
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…