Q-sets, sierpinski sets, and rapid filters

Haim Judah; Saharon Shelah

doi:10.1090/S0002-9939-1991-1045594-5

Q-sets, sierpinski sets, and rapid filters

Haim Judah
, Saharon Shelah

Einstein Institute of Mathematics

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

15 Scopus citations

Abstract

In this work we will prove the following:Theorem 1. cons(ZF) implies cons(Z.FC+ there exists a Q-set of reals + there exists a set of reals of cardinality N, which is not Lebesgue measurable). Theorem 2. cons(ZF) implies cons(ZFC + 2⁰is arbitrarily larger than H2+ there exists a Sierpinski set of cardinality 2⁰) +there are no rapid filters on a). These theorems give answers to questions of Fleissner[Fl] and Judah [Ju].

Original language	English
Pages (from-to)	821-832
Number of pages	12
Journal	Proceedings of the American Mathematical Society
Volume	111
Issue number	3
DOIs	https://doi.org/10.1090/S0002-9939-1991-1045594-5
State	Published - Mar 1991

Access to Document

10.1090/S0002-9939-1991-1045594-5

Cite this

@article{a6a1794cf49d45cda8c39b62c309126f,

title = "Q-sets, sierpinski sets, and rapid filters",

abstract = "In this work we will prove the following:Theorem 1. cons(ZF) implies cons(Z.FC+ there exists a Q-set of reals + there exists a set of reals of cardinality N, which is not Lebesgue measurable). Theorem 2. cons(ZF) implies cons(ZFC + 20is arbitrarily larger than H2+ there exists a Sierpinski set of cardinality 20) +there are no rapid filters on a). These theorems give answers to questions of Fleissner[Fl] and Judah [Ju].",

author = "Haim Judah and Saharon Shelah",

year = "1991",

month = mar,

doi = "10.1090/S0002-9939-1991-1045594-5",

language = "אנגלית",

volume = "111",

pages = "821--832",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "3",

}

TY - JOUR

T1 - Q-sets, sierpinski sets, and rapid filters

AU - Judah, Haim

AU - Shelah, Saharon

PY - 1991/3

Y1 - 1991/3

N2 - In this work we will prove the following:Theorem 1. cons(ZF) implies cons(Z.FC+ there exists a Q-set of reals + there exists a set of reals of cardinality N, which is not Lebesgue measurable). Theorem 2. cons(ZF) implies cons(ZFC + 20is arbitrarily larger than H2+ there exists a Sierpinski set of cardinality 20) +there are no rapid filters on a). These theorems give answers to questions of Fleissner[Fl] and Judah [Ju].

AB - In this work we will prove the following:Theorem 1. cons(ZF) implies cons(Z.FC+ there exists a Q-set of reals + there exists a set of reals of cardinality N, which is not Lebesgue measurable). Theorem 2. cons(ZF) implies cons(ZFC + 20is arbitrarily larger than H2+ there exists a Sierpinski set of cardinality 20) +there are no rapid filters on a). These theorems give answers to questions of Fleissner[Fl] and Judah [Ju].

UR - https://www.scopus.com/pages/publications/84968510056

U2 - 10.1090/S0002-9939-1991-1045594-5

DO - 10.1090/S0002-9939-1991-1045594-5

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:84968510056

SN - 0002-9939

VL - 111

SP - 821

EP - 832

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 3

ER -

Q-sets, sierpinski sets, and rapid filters

Abstract

Access to Document

Other files and links

Fingerprint

Cite this