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GENERIC EXISTENCE OF MAD FAMILIES

Published online by Cambridge University Press:  21 March 2017

OSVALDO GUZMÁN-GONZÁLEZ ,
MICHAEL HRUŠÁK ,
CARLOS AZAREL MARTÍNEZ-RANERO  and
ULISES ARIET RAMOS-GARCÍA
OSVALDO GUZMÁN-GONZÁLEZ
Affiliation:
CENTRO DE CIENCIAS MATEMÁTICAS UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO CAMPUS MORELIA, MORELIA MICHOACÁN 58089, MÉXICOE-mail: oguzman@matmor.unam.mx
MICHAEL HRUŠÁK
Affiliation:
INSTITUTO DE MATEMÁTICAS UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO ÁREA DE LA INVESTIGACIÓN CIENTÍFICA CIRCUITO EXTERIOR, CIUDAD UNIVERSITARIA MÉXICO 04510, D.F., MÉXICOE-mail: michael@matmor.unam.mxURL: http://www.matmor.unam.mx/∼michael
CARLOS AZAREL MARTÍNEZ-RANERO
Affiliation:
DEPARTAMENTO DE MATEMÁTICA UNIVERSIDAD DE CONCEPCIÓN CASILLA 160-C, CONCEPCIÓN, CHILEE-mail: cmartinezr@udec.cl
ULISES ARIET RAMOS-GARCÍA
Affiliation:
CENTRO DE CIENCIAS MATEMÁTICAS UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO CAMPUS MORELIA, MORELIA MICHOACÁN 58089, MÉXICOE-mail: ariet@matmor.unam.mx
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Abstract

In this note we study generic existence of maximal almost disjoint (MAD) families. Among other results we prove that Cohen-indestructible families exist generically if and only if b = c. We obtain analogous results for other combinatorial properties of MAD families, including Sacks-indestructibility and being +-Ramsey.

Keywords

Primary 03E17Secondary 03E3503E40MAD familiescardinal invariants of the continuumforcing

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Type
Articles
Information
The Journal of Symbolic Logic , Volume 82 , Issue 1 , March 2017 , pp. 303 - 316
Copyright
Copyright © The Association for Symbolic Logic 2017 

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