The exploration of graph width parameters, spanning both graph theory and algebraic frameworks, has captured substantial attention. Among these, branch width has distinctly emerged as a key metric. The Quasi-Ultrafilter serves as an axiomatic tool for scrutinizing incomplete social judgments. In this concise study, we outline a coherent definition of Quasi Ultrafilters within the connectivity system and clarify its dual association with branch width.
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Takaaki Fujita (2024) studied this question.