Near coherence of filters. II. Applications to operator ideals, the Stone-Čech remainder of a half-line, order ideals of sequences, and slenderness of groups

Blass, Andreas

doi:10.1090/S0002-9947-1987-0876466-8

Near coherence of filters. II. Applications to operator ideals, the Stone-Čech remainder of a half-line, order ideals of sequences, and slenderness of groups

Author: Andreas Blass
Journal: Trans. Amer. Math. Soc. 300 (1987), 557-581
MSC: Primary 03E05; Secondary 03C20, 03E35, 20K20, 47D25
DOI: https://doi.org/10.1090/S0002-9947-1987-0876466-8
MathSciNet review: 876466
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Abstract: The set-theoretic principle of near coherence of filters (NCF) is known to be neither provable nor refutable from the usual axioms of set theory. We show that NCF is equivalent to the following statements, among others: (1) The ideal of compact operators on Hilbert space is not the sum of two smaller ideals. (2) The Stone-Čech remainder of a half-line has only one composant. (This was first proved by J. Mioduszewski.) (3) The partial ordering of slenderness classes of abelian groups, minus its top element, is directed upward (and in fact has a top element). Thus, all these statements are also consistent and independent.

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