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SILVER ANTICHAINS

Published online by Cambridge University Press:  22 April 2015

OTMAR SPINAS  and
MAREK WYSZKOWSKI
OTMAR SPINAS
Affiliation:
DEPARTMENT OF MATHEMATICS CHRISTIAN-ALBRECHTS-UNIVERSITÄT ZU KIEL LUDEWIG-MEYN-STR. 4, 24118 KIEL, GERMANY
MAREK WYSZKOWSKI
Affiliation:
DEPARTMENT OF MATHEMATICS CHRISTIAN-ALBRECHTS-UNIVERSITÄT ZU KIEL LUDEWIG-MEYN-STR. 4, 24118 KIEL, GERMANY
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Abstract

In this paper we investigate the structure of uncountable maximal antichains of Silver forcing and show that they have to be at least of size d, where d is the dominating number. Part of this work can be used to show that the additivity of the Silver forcing ideal has size at least the unbounding number b. It follows that every reasonable amoeba Silver forcing adds a dominating real.

Keywords

Silver forcingamoeba forcingmaximal antichainbounding numberdominating number
Type
Articles
Information
The Journal of Symbolic Logic , Volume 80 , Issue 2 , June 2015 , pp. 503 - 519
Copyright
Copyright © The Association for Symbolic Logic 2015 

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References

REFERENCES

Judah, Haim, Miller, Arnold W., and Shelah, Saharon, Sacks forcing, laver forcing and martin’s axiom. Archive for Mathematical Logic, vol. 31 (1992), pp. 145–161.Google Scholar
Laguzzi, Giorgio, Some considerations on amoeba forcing notions, 2013, available athttp://www.math.uni-hamburg.de/home/laguzzi/papers/amoeba.pdfGoogle Scholar
Louveau, A., Shelah, S., and Velickovic, B., Borel partiotions of infinite sequences of perfect trees. Annals of Pure and Applied Logic, vol. 63 (1993), pp. 271–281.Google Scholar
Roslanowski, Andrzej and Shelah, Saharon, More forcing notions imply diamond. Archive for Mathematical Logic, vol. 35 (1996), pp. 299–313.Google Scholar
Simon, Petr, Sacks forcing collapses c to b. Commentationes Mathematicae Universitatis Carolinae, vol. 34 (1993), no. 4, pp. 707–710.Google Scholar