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

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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