A purely algebraic approach to total negation
by
Dean Arbuthnot & Brian McMaster
Queen's University Belfast
Coauthors: Michael Elliott

The total negation or anti-property [Paul Bankston, 1979] of a homeomorphic invariant P is the class anti-P of [homeomorphism classes of] spaces that have no P subspaces except those whose cardinalities oblige them to be P.

Mathematical arguments involving this idea are frequently so mechanical that it is natural to look for an algebraic structure to model the 'logical computations' they need, and hopefully to gain further insight into what is going on. We propose to sketch out such an algebraic object and indicate our hopes for how it will work.

Date received: May 30, 2008

Copyright © 2008 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 # cawr-14.