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15th Boise Extravaganza in Set Theory 2006
March 31 - April 2, 2006
Boise State University
Boise, ID, USA

Organizers
Liljana Babinkostova, Stefan Geschke, Justin Moore, and Marion Scheepers

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Ultra-non-filters
by
Andreas Blass
University of Michigan

By an ultra-non-filter in a Boolean algebra, I mean a subset W that is closed upward and anti-closed under complementation (i.e., x ∈ W iff (¬x) ∉ W). Other names for the same concept include "self-dual quantifier" and "maximal 2-linked family". After reviewing some known (but probably not well-known) facts about ultra-non-filters, I'll present some new results, relating the assertion "every non-degenerate Boolean algebra has an ultra-non-filter" to other weak forms of the axiom of choice.

Date received: March 14, 2006

Copyright © 2006 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # casb-07.