English

Scattered Sentences have Few Separable Randomizations

Logic 2017-04-18 v1

Abstract

In the paper "Randomizations of Scattered Sentences", Keisler showed that if Martin's axiom for aleph one holds, then every scattered sentence has few separable randomizations, and asked whether the conclusion could be proved in ZFC alone. We show here that the answer is "yes". It follows that the absolute Vaught conjecture holds if and only if every Lω1ωL_{\omega_1\omega}-sentence with few separable randomizations has countably many countable models.

Cite

@article{arxiv.1704.04981,
  title  = {Scattered Sentences have Few Separable Randomizations},
  author = {Uri Andrews and Isaac Goldbring and Sherwood Hachtman and H. Jerome Keisler and David Marker},
  journal= {arXiv preprint arXiv:1704.04981},
  year   = {2017}
}

Comments

9 pages

R2 v1 2026-06-22T19:19:07.865Z