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Ordering MAD families a la Katětov

Published online by Cambridge University Press:  12 March 2014

Michael Hrušák
Affiliation:
Instituto De Matematicas, UNAM A. P. 61-3, Xangari C. P. 58089, Morelia, Mich., Mexico, E-mail: michael@matmor.unam.mx
Salvador García Ferreira
Affiliation:
Instituto De Matematicas, UNAM A. P. 61-3, Xangari C. P. 58089, Morelia, Mich., Mexico, E-mail: sgarcia@matmor.unam.mx
Corresponding

Abstract

An ordering (≤ K ) on maximal almost disjoint (MAD) families closely related to destructibility of MAD families by forcing is introduced and studied. It is shown that the order has antichains of size c and decreasing chains of length c+ bellow every element. Assuming t = c a MAD family equivalent to all of its restrictions is constructed. It is also shown here that the Continuum Hypothesis implies that for every ω ω -bounding forcing ℙ of size c there is a Cohen-destructible, ℙ-indestructible MAD family. Finally, two other orderings on MAD families are suggested and an old construction of Mrówka is revisited.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2003

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