[FOM] question about Boolean algebras

[Vladimir Komendantsky]

Hi Neil,

Probably this data may help. In Gaetzer's book General Lattice Theory 
(1978), in II.1, Stone representation theorem (Stone, 1936) is stated in 
the form

(*) "A lattice is Boolean iff it is isomorphic to a field of sets".

It is given as a corollary of a theorem (Birkhoff, 1933; Stone, 1936)

(**) "A lattice is distributive iff it is isomorphic to a ring of sets".

Since a field of sets is such a ring of sets which is closed with 
respect to set-theoretic complement operation, Stone representation 
theorem (*) follows from the latter theorem (**) as a corollary.

Reference: [Birkhoff 1933] On the combination of subalgebras, Proc. 
Cambridge Philos. Soc., 29, 441--464.

I'm reading a translation of Graetzer's book, so statements (*) and (**) 
may be not quite the same as in the English original. But the reference 
should be the same.


Vladimir Komendantsky