Journal of Symbolic Logic

Analytic and coanalytic families of almost disjoint functions

Bart Kastermans, Juris Steprāns, and Yi Zhang

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Abstract

If ℱ ⊆ ℕ is an analytic family of pairwise eventually different functions then the following strong maximality condition fails: For any countable ℌ⊆ ℕ, no member of which is covered by finitely many functions from ℱ, there is f ∈ ℱ such that for all h∈ ℌ 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.

Article information

Source
J. Symbolic Logic Volume 73, Issue 4 (2008), 1158-1172.

Dates
First available in Project Euclid: 27 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1230396911

Digital Object Identifier
doi:10.2178/jsl/1230396911

Mathematical Reviews number (MathSciNet)
MR2467209

Zentralblatt MATH identifier
1160.03029

Citation

Kastermans, Bart; Steprāns, Juris; Zhang, Yi. Analytic and coanalytic families of almost disjoint functions. J. Symbolic Logic 73 (2008), no. 4, 1158--1172. doi:10.2178/jsl/1230396911. https://projecteuclid.org/euclid.jsl/1230396911


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