On reaping number having countable cofinality
Saharon Shelah
TL;DR
This paper proves that if the bounding number exceeds the reaping number, then the reaping number must have uncountable cofinality, revealing a new relationship between these cardinal characteristics.
Contribution
It establishes a novel result connecting the inequality of bounding and reaping numbers to the cofinality of the reaping number.
Findings
If d > r, then r has uncountable cofinality
Provides a new insight into the structure of cardinal characteristics
Enhances understanding of the relationship between bounding and reaping numbers
Abstract
We prove that if the bounding number (d) is bigger than the reaping number (r), then the latter has uncountable cofinality.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Advanced Topology and Set Theory · Mathematical and Theoretical Analysis