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Full-Text Articles in Set Theory
Minimal Sets, Union-Closed Families, And Frankl's Conjecture, Christopher S. Flippen
Minimal Sets, Union-Closed Families, And Frankl's Conjecture, Christopher S. Flippen
Theses and Dissertations
The most common statement of Frankl's conjecture is that for every finite family of sets closed under the union operation, there is some element which belongs to at least half of the sets in the family. Despite its apparent simplicity, Frankl's conjecture has remained open and highly researched since its first mention in 1979. In this paper, we begin by examining the history and previous attempts at solving the conjecture. Using these previous ideas, we introduce the concepts of minimal sets and minimally-generated families, some ideas related to viewing union-closed families as posets, and some constructions of families involving poset-defined …
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.