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Analytic and coanalytic families of almost disjoint functions

Published online by Cambridge University Press:  12 March 2014

Bart Kastermans ,
Juris Steprāns  and
Yi Zhang
Bart Kastermans
Affiliation:
Department of Mathematics, University of Wisconsin, 480 Lincoln Dr, Madison, Wi 53706-1388, USA, E-mail: [email protected] Institute of Logic and Cognition, Sun Yat-Sen University, Guangzhou, 510275, P.R.China
Juris Steprāns
Affiliation:
Department of Mathematics, York University, 4700 Keele Street, Toronto, Ontario. M3J 1P3, Canada, E-mail: [email protected] Institute of Logic and Cognition, Sun Yat-Sen University, Guangzhou, 510275, P.R.China
Yi Zhang
Affiliation:
Institute of Logic and Cognition, Sun Yat-Sen University, Guangzhou, 510275, P.R.China Department of Mathematics, Sun Yat-Sen University, Guangzhou, 510275, P.R.China, E-mail: [email protected]
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Abstract

If is an analytic family of pairwise eventually different functions then the following strong maximality condition fails: For any countable , no member of which is covered by finitely many functions from , there is such that for all there are infinitely many integers k such that f(k) = h(k). However if V = L then there exists a coanalytic family of pairwise eventually different functions satisfying this strong maximality condition.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 73 , Issue 4 , December 2008 , pp. 1158 - 1172
Copyright
Copyright © Association for Symbolic Logic 2008

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