A subalgebra B of the direct product of Boolean algebras is finitely closed if it contains along with any element f any other member of the product differing at most at finitely many places from f. Given such a B, let B* be the set of all members of B which are nonzero at each coordinate. The generalized free product corresponding to B is the subalgebra of the regular open algebra with the poset topology on B* generated by the natural basic open sets. Properties of this product are developed. The full regular open algebra is also treated.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm88-2-2,
author = {J. D. Monk},
title = {Generalized free products},
journal = {Colloquium Mathematicae},
volume = {89},
year = {2001},
pages = {175-192},
zbl = {1015.06012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm88-2-2}
}
J. D. Monk. Generalized free products. Colloquium Mathematicae, Tome 89 (2001) pp. 175-192. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm88-2-2/