Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variations of Independence in Boolean Algebras   We give a definition of some classes of boolean algebras generalizing free
boolean algebras; they satisfy a universal property that certain functions
extend to homomorphisms. We give a combinatorial property of generating sets of
these algebras, which we call n -independent. The properties of these classes
(n-free and omega-free boolean algebras) are investigated. These include
connections to hypergraph theory and cardinal invariants on these algebras.
Related cardinal functions, n Ind, which is the supremum of the cardinalities
of n-independent subsets; i_n, the minimum size of a maximal n -independent
subset; and i_omega, the minimum size of an omega-independent subset, are
introduced and investigated. The values of i_n and i_omega on P(omega)/fin are
shown to be independent of ZFC. Ideal-independence is also considered, and it
is shown that the cardinal function p <= s_mm for infinite boolean algebras. We
also define and consider moderately generated boolean algebras; that is, those
boolean algebras that have a generating set consisting of elements that split
finitely many elements of the boolean algebra.

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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg