Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Formal Theories for Linear Algebra   We introduce two-sorted theories in the style of [CN10] for the complexity
classes \oplusL and DET, whose complete problems include determinants over Z2
and Z, respectively. We then describe interpretations of Soltys' linear algebra
theory LAp over arbitrary integral domains, into each of our new theories. The
result shows equivalences of standard theorems of linear algebra over Z2 and Z
can be proved in the corresponding theory, but leaves open the interesting
question of whether the theorems themselves can be proved.

29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
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The categories of this paper are: supr-con
3
The categories of this paper are: physics