Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A simultaneous generalization of independence and disjointness 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.

17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn