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MAD SPECTRA

Published online by Cambridge University Press:  22 July 2015

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

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) $.

Type
Articles
Copyright
Copyright © The Association for Symbolic Logic 2015 

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References

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