Selection principles and the Minimal Tower problem

By Boaz Tsaban. 2001

55 citations recorded by the source corpus.

We study diagonalizations of covers using various selectionprinciples, where the covers are related to linearquasiorderings ( -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 -cover,called -cover, and settle some problems for thisvariant which are still open in the case of -covers.This new variant introduces new (and tighter) topologicaland combinatorial lower bounds on the Minimal Tower problem.

View Paper: https://www.semanticscholar.org/paper/30a952a8a6c75d11211d633845ad7c788add45e6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. Lubomyr Zdomsky
2. Boaz Tsaban
3. Marion Scheepers

Citations in the corpus

• Scales, fields, and a problem of Hurewicz (2005, background): “Many equivalences hold among these properties, and the surviving ones appear in Figure 2 (where an arrow denotes implication) [32, 19, 37].”