Advances and Applications in Discrete Mathematics
Volume 28, Issue 2, Pages 351 - 356
(November 2021) http://dx.doi.org/10.17654/DM028020351 |
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THE BOUNDING NUMBER FOR GENERALIZED REALS
Ayelet Amsalem and Adi Jarden
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Abstract: The bounding number, is one of the cardinal characteristics of the continuum. Here, we begin to study a generalized version of the bounding number.
For a set A, let denote the set of functions of A into A. Let be a cardinal. For we write when the cardinality of the set is less than The bounding number for is defined as the minimal cardinality of a -unbounded subset of This definition generalizes the definition of the bounding number which equals in our notation to
In this paper, we prove the inequality for each cardinal
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Keywords and phrases: bounding number, generalized reals, cardinal characteristics of the continuum, infinite combinatorics.
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