2.4. An arithmetic operation on bare intervals is obtained by promoting
the bare intervals to decorated intervals whose decorations are all-0 and
then performing the operation with the resulting decorated intervals.
At an abstract level, this is false as stated, because the bare intervals
are closed under arithmetic operations.
The simplest solution IMO is to assume you meant
2.4. An arithmetic operation having some bare interval operands and some
decorated interval or bare decoration operands is obtained by promoting
the bare intervals to decorated intervals whose decorations are all-0 and
then performing the operation with the resulting decorated intervals.
(Where "all-0" now becomes 4 for the bare empty set, 2 for all other bare
intervals, according to Arnold's prescription.)
Is that correct?