Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimal Constructible Sets   Given an initial family of sets, we may take unions, intersections and
complements of the sets contained in this family in order to form a new
collection of sets; our construction process is done recursively until we
obtain the last family. Problems encountered in this research include the
minimum number of steps required to arrive to the last family as well as a
characterization of that last family; we solve all those problems. We also
define a class of simple families ($n$-minimal constructible) and we analyze
the relationships between partitions and separability (our new concept) that
lead to interesting results such as finding families based on partitions that
generate finite algebras. We prove a number of new results about $n$-minimal
constructible families; one major result is that every finite algebra of sets
has a generating family which is $n$-minimal constructible for all natural $n$
and we compute the minimum number of steps required to generate an algebra.
Another interesting result is a connection between this construction process
and Baire's Theorem. This work has a number of possible applications,
particularly in the fields of economics and computer science.

8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an