Corey T. Bruns' paper explores variations of independence in Boolean algebras, focusing on n-free Boolean algebras and their properties. The paper defines n-free Boolean algebras and introduces the concept of n-independence, which is a weaker condition than independence. It also discusses the relationship between Boolean algebras and graph spaces, particularly the clique and anticlique graph spaces. The paper shows that certain Boolean algebras, such as those generated by 2-independent sets, are 2-free. It also explores the connection between Boolean algebras and hypergraphs, showing that certain hypergraphs can be used to construct Boolean algebras. The paper concludes with a discussion of the Stone dual of ω-free Boolean algebras, which are shown to be hypergraph spaces. The paper also discusses cardinal function results for Boolean algebras, including spread, character, length, cellularity, and independence. The paper provides several examples and theorems that illustrate the properties of Boolean algebras and their relationships with graphs and hypergraphs.Corey T. Bruns' paper explores variations of independence in Boolean algebras, focusing on n-free Boolean algebras and their properties. The paper defines n-free Boolean algebras and introduces the concept of n-independence, which is a weaker condition than independence. It also discusses the relationship between Boolean algebras and graph spaces, particularly the clique and anticlique graph spaces. The paper shows that certain Boolean algebras, such as those generated by 2-independent sets, are 2-free. It also explores the connection between Boolean algebras and hypergraphs, showing that certain hypergraphs can be used to construct Boolean algebras. The paper concludes with a discussion of the Stone dual of ω-free Boolean algebras, which are shown to be hypergraph spaces. The paper also discusses cardinal function results for Boolean algebras, including spread, character, length, cellularity, and independence. The paper provides several examples and theorems that illustrate the properties of Boolean algebras and their relationships with graphs and hypergraphs.