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Some Intuition Behind Large Cardinal Axioms, Their Characterization, And Related Results, Philip A. White
Some Intuition Behind Large Cardinal Axioms, Their Characterization, And Related Results, Philip A. White
Theses and Dissertations
We aim to explain the intuition behind several large cardinal axioms, give characterization theorems for these axioms, and then discuss a few of their properties. As a capstone, we hope to introduce a new large cardinal notion and give a similar characterization theorem of this new notion. Our new notion of near strong compactness was inspired by the similar notion of near supercompactness, due to Jason Schanker.
Kings In The Direct Product Of Digraphs, Morgan Norge
Kings In The Direct Product Of Digraphs, Morgan Norge
Theses and Dissertations
A k-king in a digraph D is a vertex that can reach every other vertex in D by a directed path of length at most k. A king is a vertex that is a k-king for some k. We will look at kings in the direct product of digraphs and characterize a relationship between kings in the product and kings in the factors. This is a continuation of a project in which a similar characterization is found for the cartesian product of digraphs, the strong product of digraphs, and the lexicographic product of digraphs.