[FOM] Re: small sets?

[Dmytro Taranovsky]

For every theory S (whose language includes only finitely many symbols),
the set of consistent completions of S is closed and has measure zero
(and in fact is zero dimensional in the sense of measure).

The set is perfect for every consistent recursively enumerable theory
that includes basic arithmetic.

In defining the set, the standard (or a canonical) Godel numbering is
used.

Dmytro Taranovsky