𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Forcings with the countable chain condition and the covering number of the Marczewski ideal

✍ Scribed by Teruyuki Yorioka

Book ID
105842066
Publisher
Springer
Year
2003
Tongue
English
Weight
242 KB
Volume
42
Category
Article
ISSN
0933-5846

No coin nor oath required. For personal study only.

πŸ“œ SIMILAR VOLUMES

The covering number and the uniformity o
The covering number and the uniformity of the ideal ℐf
✍ Noboru Osuga πŸ“‚ Article πŸ“… 2006 πŸ› John Wiley and Sons 🌐 English βš– 162 KB

## Abstract Let __f, g__ ∈ ^__Ο‰__^ __Ο‰__ . We will denote by __g__ ≫ __f__ that for every __k__ < __Ο‰__, __f__ (__n__ ^__k__^ ) ≀ __g__ (__n__ ) except for finitely many __n__ . The ideal ℐ~__f__~ on ^__Ο‰__^ 2 is the collection of sets __X__ such that, for some __g__ ≫ __f__ and __Ο„__ ∈ ∏~__n__ <_

A Remark on Ascending Chain Conditions,
A Remark on Ascending Chain Conditions, the Countable Axiom of Choice and the Principle of Dependent Choices
✍ Karl-Heinz Diener πŸ“‚ Article πŸ“… 1994 πŸ› John Wiley and Sons 🌐 English βš– 370 KB

## Abstract It is easy to prove in ZF^βˆ’^ (= Zermelo‐Fraenkel set theory without the axioms of choice and foundation) that a relation __R__ satisfies the maximal condition if and only if its transitive hull __R__\* does; equivalently: __R__ is well‐founded if and only if __R__\* is. We will show in