2 research outputs found
Descriptive set theory and forcing; How to prove theorems about Borel sets the hard way
These are lecture notes from a course I gave at the University of Wisconsin
during the Spring semester of 1993. Part 1 is concerned with Borel hierarchies.
Section 13 contains an unpublished theorem of Fremlin concerning Borel
hierarchies and MA. Section 14 and 15 contain new results concerning the
lengths of Borel hierarchies in the Cohen and random real model. Part 2
contains standard results on the theory of Analytic sets. Section 25 contains
Harrington's Theorem that it is consistent to have sets of arbitrary
cardinality. Part 3 has the usual separation theorems. Part 4 gives some
applications of Gandy forcing. We reverse the usual trend and use forcing
arguments instead of Baire category. In particular, Louveau's Theorem on
hyp-sets has a simpler proof using forcing