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Some applications of Hart's apophthegm
by
Ilijas Farah
York University
We prove that all autohomeomorphisms of all finite and countable powers of the Cech-Stone compactification of N, \betaN, are trivial. Under suitable set-theoretic assumptions, this result is extended to powers of \betaN\N. Similar ideas are used to prove that the R, the rectangle algebra of the Baire space need not embed into P(N)/fin. (R is the subalgebra of (P(N))N generated by the rectangles.) This solves a question of M. Bell, and gives the first known example of a Boolean algebra of `effective cardinality' not bigger than the continuum which need not embed into P(N)/fin.
Date received: June 10, 1999
Copyright © 1999 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 # cacl-70.