We study structural properties of the collection of all *σ*-ideals in the *σ*-algebra of Borel subsets of the Cantor group
$2^{\mathbb{N}}$
, especially those which satisfy the countable chain condition (ccc) and are translation invariant. We prove that the latter collection contains an uncountable family of pairwise orthogonal members and, as a consequence, a strictly decreasing sequence of length *ω*_{1}.

We also make some observations related to the *σ*-ideal *I*_{ccc} on
$2^{\mathbb{N}}$
, consisting of all Borel sets which belong to every translation invariant ccc *σ*-ideal on
$2^{\mathbb{N}}$
. In particular, improving earlier results of Recław, Kraszewski and Komjáth, we show that:

every subset of
$2^{\mathbb{N}}$
of cardinality less than
can be covered by a set from *I*_{ccc},

there exists a set *C*∈*I*_{ccc} such that every countable subset *Y* of
$2^{\mathbb{N}}$
is contained in a translate of *C*.