๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

A note on Bar Induction in Constructive Set Theory

โœ Scribed by Michael Rathjen

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
113 KB
Volume
52
Category
Article
ISSN
0044-3050

No coin nor oath required. For personal study only.

โœฆ Synopsis

Abstract

Bar Induction occupies a central place in Brouwerian mathematics. This note is concerned with the strength of Bar Induction on the basis of Constructive Zermeloโ€Fraenkel Set Theory, CZF. It is shown that CZF augmented by decidable Bar Induction proves the 1โ€consistency of CZF. This answers a question of P. Aczel who used Bar Induction to give a proof of the Lusin Separation Theorem in the constructive set theory CZF. (ยฉ 2006 WILEYโ€VCH Verlag GmbH & Co. KGaA, Weinheim)

๐Ÿ“œ SIMILAR VOLUMES

A note on stable sets, groups, and theor
A note on stable sets, groups, and theories with NIP
โœ Alf Onshuus; Ya'acov Peterzil ๐Ÿ“‚ Article ๐Ÿ“… 2007 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 152 KB ๐Ÿ‘ 1 views

## Abstract Let __M__ be an arbitrary structure. Then we say that an __M__ โ€formula __ฯ†__ (__x__) __defines a stable set in__ __M__ if every formula __ฯ†__ (__x__) โˆง __ฮฑ__ (__x__, __y__) is stable. We prove: If __G__ is an __M__ โ€definable group and every definable stable subset of __G__ has __U__ โ€

A note on stationarity of types over mod
A note on stationarity of types over models in simple theories
โœ Makoto Kobayashi; Akito Tsuboi ๐Ÿ“‚ Article ๐Ÿ“… 2008 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 81 KB ๐Ÿ‘ 1 views

## Abstract We investigate stationarity of types over models in simple theories. In particular, we show that in simple theories with finite SUโ€rank, any complete type over a model having Cantorโ€Bendixson rank is stationary. (ยฉ 2008 WILEYโ€VCH Verlag GmbH & Co. KGaA, Weinheim)