We study structural properties of the collection of all σ-ideals in the σ-algebra of Borel subsets of the Cantor group
, 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 ω1.
We also make some observations related to the σ-ideal Iccc on
, consisting of all Borel sets which belong to every translation invariant ccc σ-ideal on
. In particular, improving earlier results of Recław, Kraszewski and Komjáth, we show that:
every subset of
of cardinality less than
can be covered by a set from Iccc,
there exists a set C∈Iccc such that every countable subset Y of
is contained in a translate of C.