The Rasiowa-Sikorski lemma and the Baire property

Merry Christmas! And a Happy New Year, too. There are incredible links between logic and topology, and I would like to start with something called the Rasiowa-Sikorski lemma in logic. That is a theorem that states the existence of certain prime filters in a Boolean algebra, and which was invented as a clean justification of a completeness argument for first-order logic. Robert Goldblatt realized in a 2012 paper that the Rasiowa-Sikorski lemma is a consequence of the fact that all compact Hausdorff spaces are Baire (plus some Stone duality, which is the main bridge between logic and topology). This is a beautiful argument… read the full post.