Two Boolean algebras are elementarily equivalent if and only if they satisfy the same first-order statements in the language of Boolean algebras. We prove that every Boolean algebra is elementarily equivalent to the algebra of clopen subsets of a normal P-space.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm201-2-4, author = {Brian Wynne}, title = {The elementary-equivalence classes of clopen algebras of P-spaces}, journal = {Fundamenta Mathematicae}, volume = {201}, year = {2008}, pages = {149-161}, zbl = {1170.03017}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm201-2-4} }
Brian Wynne. The elementary-equivalence classes of clopen algebras of P-spaces. Fundamenta Mathematicae, Tome 201 (2008) pp. 149-161. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm201-2-4/