Document Type

Article

Language

eng

Format of Original

21 p.

Publication Date

6-1987

Publisher

Association for Symbolic Logic

Source Publication

Journal of Symbolic Logic

Source ISSN

0022-4812

Original Item ID

Shelves: BC1 .J6 Raynor Memorial Periodicals

Abstract

By analyzing how one obtains the Stone space of the reduced product of an indexed collection of Boolean algebras from the Stone spaces of those algebras, we derive a topological construction, the "reduced coproduct", which makes sense for indexed collections of arbitrary Tichonov spaces. When the filter in question is an ultrafilter, we show how the "ultracoproduct" can be obtained from the usual topological ultraproduct via a compactification process in the style of Wallman and Frink. We prove theorems dealing with the topological structure of reduced coproducts (especially ultracoproducts) and show in addition how one may use this construction to gain information about the category of compact Hausdorff spaces.

Comments

Published version. The Journal of Symbolic Logic, Vol. 52, No. 2 (June 1987): 404-424. Publisher Link. © The Association for Symbolic Logic 1984. Used with permission.

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