Zobrazeno 1 - 10
of 135
pro vyhledávání: '"Paolini, Gianluca"'
Autor:
Paolini, Gianluca, Shelah, Saharon
An uncountable $\aleph_1$-free group can not admit a Polish group topology but an uncountable $\aleph_1$-free abelian group can, as witnessed e.g. by the Baer-Specker group $\mathbb{Z}^\omega$. In this paper we study $\aleph_1$-free abelian non-Archi
Externí odkaz:
http://arxiv.org/abs/2410.02485
Autor:
Paolini, Gianluca, Nies, Andre
It is an open question whether topological isomorphism of oligomorphic groups is smooth in the sense of Borel reducibility. We show smoothness for two Borel classes of oligomorphic groups: groups with no algebraicity, and groups with finitely many {\
Externí odkaz:
http://arxiv.org/abs/2410.02248
Autor:
André, Simon, Paolini, Gianluca
By the work of Sela, for any free group $F$, the Coxeter group $W_ 3 = \mathbb{Z}/2\mathbb{Z} \ast \mathbb{Z}/2\mathbb{Z} \ast \mathbb{Z}/2\mathbb{Z}$ is elementarily equivalent to $W_3 \ast F$, and so Coxeter groups are not closed under elementary e
Externí odkaz:
http://arxiv.org/abs/2407.01164
Autor:
Paolini, Gianluca, Sklinos, Rizos
We prove that the irreducible affine Coxeter groups are first-order rigid and deduce from this that they are profinitely rigid in the absolute sense. We then show that the first-order theory of any irreducible affine Coxeter group does not have a pri
Externí odkaz:
http://arxiv.org/abs/2407.01141
Autor:
Paolini, Gianluca
In [21] it was asked if equality on the reals is sharp as a lower bound for the complexity of topological isomorphism between oligomorphic groups. We prove that under the assumption of weak elimination of imaginaries this is indeed the case. Our meth
Externí odkaz:
http://arxiv.org/abs/2404.04529
Autor:
Paolini, Gianluca
We prove that if $A$ is a computable Hopfian finitely presented structure, then $A$ has a computable $d$-$\Sigma_2$ Scott sentence if and only if the weak Whitehead problem for $A$ is decidable. We use this to infer that every hyperbolic group as wel
Externí odkaz:
http://arxiv.org/abs/2401.00079
Autor:
Paolini, Gianluca, Shelah, Saharon
In [9] we proved that the space of countable torsion-free abelian groups is Borel complete. In this paper we show that our construction from [9] satisfies several additional properties of interest. We deduce from this that countable torsion-free abel
Externí odkaz:
http://arxiv.org/abs/2312.04162
Autor:
Nation, J. B., Paolini, Gianluca
We start a systematic analysis of the first-order model theory of free lattices. Firstly, we prove that the free lattices of finite rank are not positively indistinguishable, as there is a positive $\exists \forall$-sentence true in $\mathbf F_3$ and
Externí odkaz:
http://arxiv.org/abs/2310.03366
Autor:
Carolillo, Davide, Paolini, Gianluca
In [11] Sklinos proved that any uncountable free group is not $\aleph_1$-homogenenous. This was later generalized by Belegradek in [1] to torsion-free residually finite relatively free groups, leaving open whether the assumption of residual finitenes
Externí odkaz:
http://arxiv.org/abs/2307.10692
Autor:
Paolini, Gianluca, Shelah, Saharon
Relying on the techniques and ideas from our recent paper [13], we prove several anti-classification results for various rigidity conditions in countable abelian and nilpotent groups. We prove three main theorems: (1) the rigid abelian groups are com
Externí odkaz:
http://arxiv.org/abs/2303.03778