The generic ultrafilter added by ${(\FIN \times \FIN)}^{+}$

Dilip Raghavan

The generic ultrafilter added by ${(\FIN \times \FIN)}^{+}$

Logic 2012-10-30 v1

Authors: Dilip Raghavan

Abstract

We investigate the Tukey type of the generic ultrafilter added by the quotient $\mathcal{P}(\omega \times \omega) / (\mathrm{FIN} \times \mathrm{FIN})$ . We prove that this ultrafilter is not basically generated and yet does not have the maximal Tukey type among directed partial orders of size continuum. Moreover, any Tukey reduction from this ultrafilter to any other ultrafilter is witnessed by a Baire class one map.

Keywords

generic ultrafilter Tukey type quotient algebra Baire class one map directed partial orders set theory

Cite

@article{arxiv.1210.7387,
  title  = {The generic ultrafilter added by ${(\FIN \times \FIN)}^{+}$},
  author = {Dilip Raghavan},
  journal= {arXiv preprint arXiv:1210.7387},
  year   = {2012}
}

Comments

Preliminary

The generic ultrafilter added by ${(\FIN \times \FIN)}^{+}$

Abstract

Keywords

Cite

Comments

Related papers