Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-08T02:34:00.575Z Has data issue: false hasContentIssue false
  • English
  • Français

MAD SPECTRA

Published online by Cambridge University Press:  22 July 2015

SAHARON SHELAH  and
OTMAR SPINAS
SAHARON SHELAH
Affiliation:
EINSTEIN INSTITUTE OF MATHEMATICS EDMOND J. SAFRA CAMPUS, GIVAT RAM THE HEBREW UNIVERSITY OF JERUSALEM JERUSALEM, 91904, ISRAEL and DEPARTMENT OF MATHEMATICS HILL CENTER - BUSCH CAMPUS, RUTGERS THE STATE UNIVERSITY OF NEW JERSEY 110 FRELINGHUYSEN ROAD PISCATAWAY, NJ 08854-8019, USA
OTMAR SPINAS
Affiliation:
MATHEMATISCHES SEMINAR DER CHRISTIAN-ALBRECHTS-UNIVERSITÄT ZU KIEL LUDEWIG-MEYN-STRAßE 424118 KIEL, GERMANY
Get access Rights & Permissions [Opens in a new window]

Abstract

The mad spectrum is the set of all cardinalities of infinite maximal almost disjoint families on ω. We treat the problem to characterize those sets ${\rm {\cal A}} $ which, in some forcing extension of the universe, can be the mad spectrum. We give a complete solution to this problem under the assumption $\vartheta ^{ < \vartheta } = \vartheta $, where $\vartheta = {\rm{min}}\left( {\rm {\cal A}} \right) $.

Keywords

Primary: 03E3503E17set theoryforcingMAD familiesset theory of the reals
Type
Articles
Information
The Journal of Symbolic Logic , Volume 80 , Issue 3 , September 2015 , pp. 901 - 916
Copyright
Copyright © The Association for Symbolic Logic 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Brendle, Jörg, The almost-disjointness number may have countable cofinality. Transactions of the American Mathematical Society 355, vol. no. 7 (2003), pp. 2633–2649.CrossRefGoogle Scholar
Hechler, Stephen S., Short complete nested sequences in βn \ n and small maximal almost-disjoint families. General Topology and its Applications, vol. 2 (1972), pp. 139–149.CrossRefGoogle Scholar
Shelah, Saharon, Special subsets of cf(μ)μ, boolean algebras and maharam measure algebras. Topology and its Application, vol. 99 (1999), pp. 135–235.CrossRefGoogle Scholar
Shelah, Saharon, Two cardinal invariants of the continuum $\left( {{\rm } < {\rm }} \right) $and fs linearly ordered iterated forcing. Acta Mathematica, vol. 192 (2004), pp. 187–233.CrossRefGoogle Scholar