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

Arch. Math. Logic 43, 991–1008 (2004) Digital Object Identifier (DOI): 10.1007/s00153-004-0244-0

Mathematical Logic

Iraj Kalantari · Larry Welch

A blend of methods of recursion theory and topology: A
01 tree of shadow points Received: 13 June 2003 / Revised version: 18 December 2003 / Published online: 28 May 2004 – © Springer-Verlag 2004 Abstract. This paper is a sequel to our [7]. In that paper we constructed a
01 tree of avoidable points. Here we construct a
01 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