Transitive properties of the ideal S2.

Abstract

In this paper we compute transitive cardinal coefficients of the $\sigma$-ideal $\mathbb{S}_2$, the least nontrivial productive $\sigma$-ideal of subsets of the Cantor space $2^\omega$. We also apply transitive operations to $\mathbb{S}_2$. In particular, we show that $\sigma$-ideal of strongly $\mathbb{S}_2$ sets is equal to $\mathbb{B}2$, one of Mycielski ideals.