Journal of Symbolic Logic 51 (3):560-569 (1986)

Abstract
Let J be any proper ideal of subsets of the real line R which contains all finite subsets of R. We define an ideal J * ∣B as follows: X ∈ J * ∣B if there exists a Borel set $B \subset R \times R$ such that $X \subset B$ and for any x ∈ R we have $\{y \in R: \langle x,y\rangle \in B\} \in \mathscr{J}$ . We show that there exists a family $\mathscr{A} \subset \mathscr{J}^\ast\mid\mathscr{B}$ of power ω 1 such that $\bigcup\mathscr{A} \not\in \mathscr{J}^\ast\mid\mathscr{B}$ . In the last section we investigate properties of ideals of Lebesgue measure zero sets and meager sets in Cohen extensions of models of set theory
Keywords Lebesgue measure   Baire category   cardinal indices   Cohen reals
Categories (categorize this paper)
DOI 10.2307/2274013
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 72,564
Through your library

References found in this work BETA

Internal Cohen Extensions.D. A. Martin & R. M. Solovay - 1970 - Annals of Mathematical Logic 2 (2):143-178.
Descriptive Set Theory.Yiannis Nicholas Moschovakis - 1982 - Studia Logica 41 (4):429-430.
Boolean Algebras.Roman Sikorski - 1966 - Journal of Symbolic Logic 31 (2):251-253.
Set Theory.H. B. Enderton - 1975 - Journal of Symbolic Logic 40 (4):629-630.

Add more references

Citations of this work BETA

Combinatorial Properties of Hechler Forcing.Jörg Brendle, Haim Judah & Saharon Shelah - 1992 - Annals of Pure and Applied Logic 58 (3):185-199.
Van Douwen’s Diagram for Dense Sets of Rationals.Jörg Brendle - 2006 - Annals of Pure and Applied Logic 143 (1-3):54-69.
Combinatorial Properties of Classical Forcing Notions.Jörg Brendle - 1995 - Annals of Pure and Applied Logic 73 (2):143-170.
Localizations of Infinite Subsets of $\omega$.Andrzej Rosłanowski & Saharon Shelah - 1996 - Archive for Mathematical Logic 35 (5-6):315-339.
On Monotone Hull Operations.Marek Balcerzak & Tomasz Filipczak - 2011 - Mathematical Logic Quarterly 57 (2):186-193.

View all 7 citations / Add more citations

Similar books and articles

On the T-Degrees of Partial Functions.Paolo Casalegno - 1985 - Journal of Symbolic Logic 50 (3):580-588.
The Reals in Core Models.Philip Welch - 1987 - Journal of Symbolic Logic 52 (1):64-67.
Cohen-Stable Families of Subsets of Integers.Miloš S. Kurilić - 2001 - Journal of Symbolic Logic 66 (1):257-270.
U-Lusin Sets in Hyperfinite Time Lines.Renling Jin - 1992 - Journal of Symbolic Logic 57 (2):528-533.
Existence of Some Sparse Sets of Nonstandard Natural Numbers.Renling Jin - 2001 - Journal of Symbolic Logic 66 (2):959-973.

Analytics

Added to PP index
2009-01-28

Total views
217 ( #54,160 of 2,533,482 )

Recent downloads (6 months)
1 ( #391,480 of 2,533,482 )

How can I increase my downloads?

Downloads

My notes