Skip to main content Accessibility help
×
Home

Splitting Families and Complete Separability

  • Heike Mildenberger (a1), Dilip Raghavan (a2) and Juris Steprans (a3)

Abstract

We answer a question from Raghavan and Steprāns by showing that $\mathfrak{s}\,\text{=}\,{{\mathfrak{s}}_{\omega ,\omega }}.$ Then we use this to construct a completely separable maximal almost disjoint family under $\mathfrak{s}\,\le \,\mathfrak{a}$ , partially answering a question of Shelah.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Splitting Families and Complete Separability
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Splitting Families and Complete Separability
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Splitting Families and Complete Separability
      Available formats
      ×

Copyright

References

Hide All
[1] Balcar, B., Dočkálková, J., and Simon, P., Almost disjoint families of countable sets. In: Finite and infinite sets, Vol. I, II (Eger, 1981), Colloq. Math. Soc. János Bolyai 37, North-Holland, Amsterdam, 1984, 5988.
[2] Balcar, B. and Simon, P., Disjoint refinement. In: Handbook of Boolean algebras, Vol. 2, North-Holland, Amsterdam, 1989, 333388.
[3] Erdős, P. and Shelah, S., Separability properties of almost-disjoint families of sets. Israel J. Math. 12 (1972), 207214. http://dx.doi.org/10.1007/BF02764666
[4] Kamburelis, A. and Węglorz, B., Splittings. Arch. Math. Logic 35 (1996), 263277. http://dx.doi.org/10.1007/s001530050044
[5] Raghavan, D. and Steprāns, J., On weakly tight families. Canad. J. Math., to appear. http://dx.doi.org/10.4153/CJM-2012-017-8
[6] Shelah, S., Mad families and sane player. Preprint, 0904.0816.
[7] Simon, P., A note on almost disjoint refinement. In: 24thWinter School on Abstract Analysis (Benešova Hora, 1996), Acta Univ. Carolin. Math. Phys. 37 (1996), 8999.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Keywords

Related content

Powered by UNSILO

Splitting Families and Complete Separability

  • Heike Mildenberger (a1), Dilip Raghavan (a2) and Juris Steprans (a3)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.