Selection principles and the Minimal Tower problem

Authors

  • Boaz Tsaban

DOI:

https://doi.org/10.1285/i15900932v22n2p53

Keywords:

Gerlits-Nagy property $gamma$-sets, $gamma$-cover, $omega$-cover, $ au$-cover, Tower, Selection principles, Borel covers, Open covers

Abstract

We study diagonalizations of covers using various selectionprinciples, where the covers are related to linearquasiorderings ($\tau$-covers).This includes: equivalences and nonequivalences,combinatorial characterizations, critical cardinalities andconstructions of special sets of reals.This study leads to a solution of a topological problem which wassuggested to the author by Scheepers (and stated in [15]) and is related to the Minimal Tower problem.

We also introduce a variant of the notion of $\tau$-cover,called $\tau^*$-cover, and settle some problems for thisvariant which are still open in the case of $\tau$-covers.This new variant introduces new (and tighter) topologicaland combinatorial lower bounds on the Minimal Tower problem.

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Published

29-10-2003

Issue

Volume 22, Issue 2 (2003)

Section

Articoli

License

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