Archive for Mathematical Logic 58 (7-8):1035-1051 (2019)

Abstract
We investigate maximal free sequences in the Boolean algebra \ {/}\text {fin}\), as defined by Monk :593–610, 2011). We provide some information on the general structure of these objects and we are particularly interested in the minimal cardinality of a free sequence, a cardinal characteristic of the continuum denoted \. Answering a question of Monk, we demonstrate the consistency of \. In fact, this consistency is demonstrated in the model of Shelah for \ :433–443, 1992). Our paper provides a streamlined and mostly self contained presentation of this construction.
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DOI 10.1007/s00153-019-00675-w
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References found in this work BETA

Con(U>I).Saharon Shelah - 1992 - Archive for Mathematical Logic 31 (6):433-443.
Ramsey Ultrafilters and the Reaping Number—Con.M. Goldstern & S. Shelah - 1990 - Annals of Pure and Applied Logic 49 (2):121-142.

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