Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum mechanics over sets   In the tradition of toy models of quantum mechanics in vector spaces over
finite fields (e.g., Schumacher and Westmoreland's "modal quantum theory"), one
finite field stands out, 2, since vectors over 2 have an interpretation as
natural mathematical objects, i.e., sets. This engages a sets-to-vector-spaces
bridge that is part of the mathematical folklore to translate both ways between
set concepts and vector space concepts. Using that bridge, the mathematical
framework of (finite-dimensional) quantum mechanics can be transported down to
sets resulting in quantum mechanics over sets or QM/sets. This approach leads
to a different treatment of Dirac's brackets than in "modal quantum theory"
(MQT), and that gives a full probability calculus (unlike MQT that only has
zero-one modalities of impossible and possible). That, in turn, leads to a
rather fulsome theory of QM over sets that includes "logical" models of the
double-slit experiment, Bell's Theorem, quantum information theory, quantum
computing, and much else. Indeed, QM/sets is proposed as the "logic" of QM in
the old-fashioned sense of "logic" as giving the simplified essentials of a
theory. QM/sets is also a key part of a broader research program to provide an
interpretation of QM based on the notion of "objective indefiniteness," a
program that grew out the recent development of the logic of partitions
mathematically dual to the usual Boolean logic of subsets.

2
The categories of this paper are: math
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
18
The categories of this paper are: econ
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph