Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Some properties of measure and category


Author: Arnold W. Miller
Journal: Trans. Amer. Math. Soc. 266 (1981), 93-114
MSC: Primary 03E35; Secondary 03E15, 28C15, 54A35, 54H05
DOI: https://doi.org/10.1090/S0002-9947-1981-0613787-2
MathSciNet review: 613787
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Several elementary cardinal properties of measure and category on the real line are studied. For example, one property is that every set of real numbers of cardinality less than the continuum has measure zero. All of the properties are true if the continuum hypothesis is assumed. Several of the properties are shown to be connected with the properties of the set of functions from integers to integers partially ordered by eventual dominance. Several, but not all, combinations of these properties are shown to be consistent with the usual axioms of set theory. The main technique used is iterated forcing.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 03E35, 03E15, 28C15, 54A35, 54H05

Retrieve articles in all journals with MSC: 03E35, 03E15, 28C15, 54A35, 54H05


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1981-0613787-2
Article copyright: © Copyright 1981 American Mathematical Society