Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Irreducible Truth-Value Algebras Suffice for the Completeness of Many
  First-Order Algebraic Logics   It is well-known that a Hilbert-style deduction system for first-order
classical logic is sound and complete for a model theory built using all
Boolean algebras as truth-value algebras if and only if it is sound and
complete for a model theory utilizing only irreducible Boolean algebras (which
are all isomorphic to the two-element Boolean algebra). In this paper, we prove
an analogous result for any first-order logic with an algebraic semantics
satisfying certain minimal assumptions, and we then apply our result to
first-order quantum logic.

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The categories of this paper are: econ
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The categories of this paper are: hep-lat
3
The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex