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On the number of |
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| Authors: | Saharon Shelah Pauli Vä isä nen |
| Affiliation: | Institute of Mathematics, The Hebrew University, Jerusalem, Israel and Rutgers University, Hill Ctr-Busch, New Brunswick, New Jersey 08903 ; Department of Mathematics, P.O. Box 4, 00014 University of Helsinki, Finland |
| Abstract: | We prove that if |
| Keywords: | Number of models ladder system uniformization infinitary logic iterated forcing |
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is consistent then 
is consistent with the following statement: There is for every 
a model of cardinality 
which is 
-equivalent to exactly 
non-isomorphic models of cardinality 
. In order to get this result we introduce ladder systems and colourings different from the ``standard' counterparts, and prove the following purely combinatorial result: For each prime number 
and positive integer 
it is consistent with 
that there is a ``good' ladder system having exactly 
pairwise nonequivalent colourings.