A null ideal for inaccessibles

A null ideal for inaccessibles In this paper we introduce a tree-like forcing notion extending some properties of the random forcing in the context of $$2^\kappa $$ 2 κ , $$\kappa $$ κ inaccessible, and study its associated ideal of null sets and notion of measurability. This issue was addressed by Shelah (On CON(Dominating $$\_$$ _ lambda $$\,>\,$$ > cov $$\_\lambda $$ _ λ (meagre)), arXiv:0904.0817 , Problem 0.5) and concerns the definition of a forcing which is $$\kappa ^\kappa $$ κ κ -bounding, $$<\kappa $$ < κ -closed and $$\kappa ^+$$ κ + -cc, for $$\kappa $$ κ inaccessible. Cohen and Shelah (Generalizing random real forcing for inaccessible cardinals, arXiv:1603.08362 ) provide a proof for (Shelah, On CON(Dominating $$\_$$ _ lambda $$\,>\,$$ > cov $$\_\lambda $$ _ λ (meagre)), arXiv:0904.0817 , Problem 0.5), and in this paper we independently reprove this result by using a different type of construction. This also contributes to a line of research adressed in the survey paper (Khomskii et al. in Math L Q 62(4–5):439–456, 2016). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Mathematical Logic Springer Journals

A null ideal for inaccessibles

Loading next page...
 
/lp/springer_journal/a-null-ideal-for-inaccessibles-45Gxer9meT
Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2017 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Mathematical Logic and Foundations; Mathematics, general; Algebra
ISSN
0933-5846
eISSN
1432-0665
D.O.I.
10.1007/s00153-017-0562-7
Publisher site
See Article on Publisher Site

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches

$49/month

Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.

$588

$360/year

billed annually
Start Free Trial

14-day Free Trial