P. Leonetti

Complexity and Polishability of characterized subgroups on the unit circle

Given an ideal $\mathcal I$ on $\omega$, a subgroup $H$ of the unit circle $\mathbb T$ is said to be $\mathcal I$-characterized if there exists a sequence of integers $(a_n:n\in\omega)$ such that $$ H= \left\{ x\in\mathbb T: \mathcal I\text{-}\lim_{n\to\infty}a_nx=0 \right\}. $$ We investigate the descriptive complexit...