Lindelöf models of the reals: Solution to a problem of Sikorski

Larry Manevitz; Arnold W. Miller

doi:10.1007/BF02774017

Lindelöf models of the reals: Solution to a problem of Sikorski

Larry Manevitz, Arnold W. Miller

Research output: Contribution to journal › Article › peer-review

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Abstract

We show that it is consistent with ZFC that there is a model M of ZF + DC such that the integers of M are ω₁-like, the reals of M have cardinality ω₂, and the unit interval [0, 1]^M is Lindelöf (i.e. every open cover has a countable subcover). This answers an old question of Sikorski.

Original language	English
Pages (from-to)	209-218
Number of pages	10
Journal	Israel Journal of Mathematics
Volume	45
Issue number	2-3
DOIs	https://doi.org/10.1007/BF02774017
State	Published - Jun 1983
Externally published	Yes

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title = "Lindel{\"o}f models of the reals: Solution to a problem of Sikorski",

abstract = "We show that it is consistent with ZFC that there is a model M of ZF + DC such that the integers of M are ω 1-like, the reals of M have cardinality ω 2, and the unit interval [0, 1] M is Lindel{\"o}f (i.e. every open cover has a countable subcover). This answers an old question of Sikorski.",

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year = "1983",

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N2 - We show that it is consistent with ZFC that there is a model M of ZF + DC such that the integers of M are ω 1-like, the reals of M have cardinality ω 2, and the unit interval [0, 1] M is Lindelöf (i.e. every open cover has a countable subcover). This answers an old question of Sikorski.

AB - We show that it is consistent with ZFC that there is a model M of ZF + DC such that the integers of M are ω 1-like, the reals of M have cardinality ω 2, and the unit interval [0, 1] M is Lindelöf (i.e. every open cover has a countable subcover). This answers an old question of Sikorski.

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Lindelöf models of the reals: Solution to a problem of Sikorski

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