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SILVER ANTICHAINS

  • OTMAR SPINAS (a1) and MAREK WYSZKOWSKI (a1)

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.

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[1]Judah, Haim, Miller, Arnold W., and Shelah, Saharon, Sacks forcing, laver forcing and martin’s axiom. Archive for Mathematical Logic, vol. 31 (1992), pp. 145161.
[2]Laguzzi, Giorgio, Some considerations on amoeba forcing notions, 2013, available athttp://www.math.uni-hamburg.de/home/laguzzi/papers/amoeba.pdf
[3]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. 271281.
[4]Roslanowski, Andrzej and Shelah, Saharon, More forcing notions imply diamond. Archive for Mathematical Logic, vol. 35 (1996), pp. 299313.
[5]Simon, Petr, Sacks forcing collapses c to b. Commentationes Mathematicae Universitatis Carolinae, vol. 34 (1993), no. 4, pp. 707710.

Keywords

SILVER ANTICHAINS

  • OTMAR SPINAS (a1) and MAREK WYSZKOWSKI (a1)

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