English

Unreachability of $\bf{\Gamma_{2n+1,m}}$

Logic 2023-12-04 v1

Abstract

We find bounds for the maximal length of a sequence of distinct Γ2n+1,m\bf{\Gamma_{2n+1,m}}-sets under ADAD and show there is no sequence of distinct Γ2n+1\bf{\Gamma_{2n+1}}-sets of length δ2n+31\bf{\delta^1_{2n+3}}. As a special case, there is no sequence of distinct Γ1,m\bf{\Gamma_{1,m}}-sets of length m+2\aleph_{m+2}. These are the optimal results for the pointclasses Γ2n+1\bf{\Gamma_{2n+1}} and Γ1,m\bf{\Gamma_{1,m}}.

Keywords

Cite

@article{arxiv.2312.00278,
  title  = {Unreachability of $\bf{\Gamma_{2n+1,m}}$},
  author = {Derek Levinson},
  journal= {arXiv preprint arXiv:2312.00278},
  year   = {2023}
}