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  1.  17
    Free Sequences in $${Mathscr {P}}Left /Text {Fin}$$ P Ω / Fin.David Chodounský, Vera Fischer & Jan Grebík - 2019 - Archive for Mathematical Logic 58 (7-8):1035-1051.
    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 (...)
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  2.  11
    Free sequences in $${\mathscr {P}}\left( \omega \right) /\text {fin}$$.David Chodounský, Vera Fischer & Jan Grebík - 2019 - Archive for Mathematical Logic 58 (7):1035-1051.
    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 (...)
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    Free sequences in $${mathscr {P}}left /text {fin}$$ P ω / fin.David Chodounský, Vera Fischer & Jan Grebík - 2019 - Archive for Mathematical Logic 58 (7):1035-1051.
    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 (...)
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    Bases and Borel Selectors for Tall Families.Jan Grebík & Carlos Uzcátegui - 2019 - Journal of Symbolic Logic 84 (1):359-375.
    Given a family${\cal C}$of infinite subsets of${\Bbb N}$, we study when there is a Borel function$S:2^{\Bbb N} \to 2^{\Bbb N} $such that for every infinite$x \in 2^{\Bbb N} $,$S\left \in {\Cal C}$and$S\left \subseteq x$. We show that the family of homogeneous sets as given by the Nash-Williams’ theorem admits such a Borel selector. However, we also show that the analogous result for Galvin’s lemma is not true by proving that there is an$F_\sigma $tall ideal on${\Bbb N}$without a Borel selector. The (...)
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