DOIAbstract
summary:We study free sequences and related notions on Boolean algebras. A free sequence on a BA $A$ is a sequence $\langle a_\xi:\xi< \alpha \rangle$ of elements of $A$, with $\alpha$ an ordinal, such that for all $F,G\in[\alpha]^{<\omega}$ with $F<G$ we have $\prod_{\xi\in F}a_\xi\cdot \prod_{\xi\in G}-a_\xi \not=0$. A free sequence of length $\alpha$ exists iff the Stone space $\operatorname{Ult}(A)$ has a free sequence of length $\alpha $ in the topological sense. A free sequence is maximal iff it cannot be extended at the end to a longer free sequence. The main notions studied here are the spectrum function $$ {\frak f}_{\operatorname{sp}}(A)=\{|\alpha|:A\hbox{ has an infinite maximal free sequence of length }\alpha \} $$ and the assoc...
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