𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the conservativity of the axiom of choice over set theory

✍ Scribed by Timothy J. Carlson

Publisher
Springer
Year
2011
Tongue
English
Weight
219 KB
Volume
50
Category
Article
ISSN
0933-5846

No coin nor oath required. For personal study only.

πŸ“œ SIMILAR VOLUMES

On the axiom of extensionality in the po
On the axiom of extensionality in the positive set theory
✍ Olivier Esser πŸ“‚ Article πŸ“… 2003 πŸ› John Wiley and Sons 🌐 English βš– 102 KB πŸ‘ 1 views

## Abstract This is a study of the relative interpretability of the axiom of extensionality in the positive set theory. This work has to be considered in the line of works of R. O. Gandy, D. Scott and R. Hinnion who have studied the relative interpretability of the axiom of extensionality in set th

Bases, spanning sets, and the axiom of c
Bases, spanning sets, and the axiom of choice
✍ Paul Howard πŸ“‚ Article πŸ“… 2007 πŸ› John Wiley and Sons 🌐 English βš– 171 KB πŸ‘ 1 views

## Abstract Two theorems are proved: First that the statement β€œthere exists a field __F__ such that for every vector space over __F__, every generating set contains a basis” implies the axiom of choice. This generalizes theorems of Halpern, Blass, and Keremedis. Secondly, we prove that the assert

The axiom of choice and the law of exclu
The axiom of choice and the law of excluded middle in weak set theories
✍ John L. Bell πŸ“‚ Article πŸ“… 2008 πŸ› John Wiley and Sons 🌐 English βš– 116 KB πŸ‘ 1 views

## Abstract A weak form of intuitionistic set theory **WST** lacking the axiom of extensionality is introduced. While **WST** is too weak to support the derivation of the law of excluded middle from the axiom of choice, we show that bee.ng up **WST** with moderate extensionality principles or quoti