English

Determinacy and \Delta^1_3-degrees

Logic 2016-09-06 v1

Abstract

Let D = { d_n } be a countable collection of Delta^1_3 degrees. Assuming that all co-analytic games on integers are determined (or equivalently that all reals have ``sharps''), we prove that either D has a Delta^1_3-minimal upper bound, or that for any n, and for every real r recursive in d_n, games in the pointclasses Delta^1_2(r) are determined. This is proven using Core Model theory.

Keywords

Cite

@article{arxiv.math/9608203,
  title  = {Determinacy and \Delta^1_3-degrees},
  author = {Philip Welch},
  journal= {arXiv preprint arXiv:math/9608203},
  year   = {2016}
}