✦ LIBER ✦

Contents: Math. Log. Quart. 5/2008

Publisher: John Wiley and Sons
Year: 2008
Tongue: English
Weight: 79 KB
Volume: 54
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200810400

No coin nor oath required. For personal study only.

✦ Synopsis

Various types of continuity for preference relations on a metric space are examined constructively. In particular, necessary and sufficient conditions are given for an order-dense, strongly extensional preference relation on a complete metric space to be continuous. It is also shown, in the spirit of constructive reverse mathematics, that the continuity of sequentially continuous, order-dense preference relations on complete, separable metric spaces is connected to Ishihara's principle BD-N, and therefore is not provable within Bishop-style constructive mathematics alone.

📜 SIMILAR VOLUMES

Contents: Math. Log. Quart. 1/2008

📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 57 KB

## The Relation Reflection Scheme We introduce a new axiom scheme for constructive set theory, the Relation Reflection Scheme (RRS). Each instance of this scheme is a theorem of the classical set theory ZF. In the constructive set theory CZF -, when the axiom scheme is combined with the axiom of D

Contents: Math. Log. Quart. 2/2008

📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 71 KB

Contents: Math. Log. Quart. 3/2008

📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 67 KB

Contents: Math. Log. Quart. 4/2008

📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 67 KB

## Groupwise density cannot be much bigger than the unbounded number We prove that g (the groupwise density number) is smaller or equal to b + , the successor of the minimal cardinality of an unbounded subset of ω ω. This is true even for the version of g for groupwise dense ideals.

Contents: Math. Log. Quart. 6/2008

📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 71 KB

On the Π 1 1 -separation principle We study the proof-theoretic strength of the Π 1 1 -separation axiom scheme, and we show that Π 1 1 -separation lies strictly in between the Δ 1 1 -comprehension and Σ 1 1 -choice axiom schemes over RCA 0 .

Editorial: Math. Log. Quart. 5/2008

✍ Vasco Brattka; Hajime Ishihara; Matthias Schröder; Ning Zhong 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 16 KB