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Binary Partitions in the Absence of Choice or Rearranging Russell's Socks
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Horst HerrlichGiven a sequence (Xn )n∈N of pairwise disjoint 2-element sets. Can ∪ n∈N Xn be rearranged as a union ∪ i∈I Yi of a family (Yi )i∈I of pairwise disjoint 2-element sets, indexed by an uncountable set I? It... -
On Russell and Anti Russell-Cardinals
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Horst Herrlich --- , Germany Kyriakos Keremedis --- Department of Mathematics, Greece Eleftherios Tachtsis --- Department of Statistics and Actuarial-Financial Mathematics, GreeceIn the absence of the Axiom of Choice we study countable families of 2-element sets with no choice functions which either have infinite subfamilies with a choice function or no infinite subfamilies with a choice function. -
An Independence Result Concerning Russell-Cardinals
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Eleftherios TachtsisWe show that it is consistent with ZF 0 that there exists a Russell-cardinal α such that the cardinals α 2 and 2α are incomparable. This answers in the negative a related question from Herrlich and Tachtsis “On the number... -
An assessment of behavioural dominance in a social subterranean rodent, Cryptomys hottentotus pretoriae, using the cardinal dominance index method
Item type: Journal Article • Journal: African Zoology • Authors: G. P. Malherbe --- Department of Zoology and Entomology, South Africa N. C. Bennett --- Department of Zoology and Entomology, South AfricaThe highveld mole-rat, Cryptomys hottentotus pretoriae, is a social bathyergid that exhibits a high reproductive skew and occurs in colonies of between 5 and 14 individuals. Behavioural dominance has previously been assessed in this species using an ordinal ranking procedure... -
More on cardinality bounds involving the weak Lindelöf degree
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: A. Bella --- University of Catania, Italy N. Carlson --- California Lutheran University, USA I. Gotchev --- Central Connecticut State University, USAWe give several new bounds for the cardinality of a Hausdorff topological space X involving the weak Lindelöf degree ωL(X). In particular, we show that if X is extremally disconnected, then |X| ≤ 2 ωL (X)πχ(X)ψ(X), and if X...