# Sh:723

• Shelah, S. (2001). Consistently there is no non trivial ccc forcing notion with the Sacks or Laver property. Combinatorica, 21(2), 309–319.
• Abstract:
The result in the title answers a problem of Boban Velickovic. A definable version of it (that is for Souslin forcing notions) has been answered in [Sh 480], and our proof follows it. Independently Velickovic proved this consistency, following [Sh 480] and some of his works, proving it from PFA and from OCA. We prove that moreover, consistently there is no ccc forcing with the Laver property. Note that if cov(meagre)=continuum (which follows e.g. from PFA) then there is a (non principal) Ramsey ultrafilter on \omega hence a forcing notion with the Laver property. So the results are incomparable.
• Version 2000-03-13_11 (8p) published version (11p)
Bib entry
@article{Sh:723,
author = {Shelah, Saharon},
title = {{Consistently there is no non trivial ccc forcing notion with the Sacks or Laver property}},
journal = {Combinatorica},
fjournal = {Combinatorica. An International Journal on Combinatorics and the Theory of Computing},
volume = {21},
number = {2},
year = {2001},
pages = {309--319},
issn = {0209-9683},
mrnumber = {1832454},
mrclass = {03E05 (03E35)},
doi = {10.1007/s004930100027},
note = {\href{https://arxiv.org/abs/math/0003139}{arXiv: math/0003139}},
arxiv_number = {math/0003139},
conference = {Paul Erd\H{o}s and his mathematics (Budapest, 1999)}
}