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The Distributivity Numbers of P(ω)/FIN and Its Square

Saharon Shelah and Otmar Spinas
Transactions of the American Mathematical Society
Vol. 352, No. 5 (May, 2000), pp. 2023-2047
Stable URL: http://www.jstor.org/stable/118122
Page Count: 25
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The Distributivity Numbers of P(ω)/FIN and Its Square
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Abstract

We show that in a model obtained by forcing with a countable support iteration of Mathias forcing of length ω 2, the distributivity number of P(ω)/fin is ω 2, whereas the distributivity number of r.o.(P(ω)/fin)2 is ω 1. This answers a problem of Balcar, Pelant and Simon, and others.

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