A blend of methods of recursion theory and topology: A П 0^1 tree of shadow points

✍ Scribed by Iraj Kalantari; Larry Welch

• Publisher: Springer
• Year: 2004
• Tongue: English
• Weight: 610 KB
• Volume: 43
• Category: Article
• ISSN: 0933-5846
• DOI: 10.1007/s00153-004-0244-0

✦ Synopsis

This paper is a sequel to our [7]. In that paper we constructed a 0 1 tree of avoidable points. Here we construct a 0 1 tree of shadow points. This tree is a tree of sharp filters, where a sharp filter is a nested sequence of basic open sets converging to a point. In the construction we assign to each basic open set on the tree an address in 2 <ω . One interesting fact is that while our 0 1 tree of sharp filters (a subtree of <ω ) is isomorphic to the tree of addresses (a subtree of 2 <ω ), the tree of addresses is recursively enumerable but not recursive.

To achieve this end we use a finite injury priority argument.