Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classical logic and intuitionistic logic: equivalent formulations in
  natural deduction, G\"odel-Kolmogorov-Glivenko translation   This report first shows the equivalence bewteen several formulations of
classical logic in intuitionistic logic (tertium non datur, reductio ad
absurdum, Pierce's law). Then it establishes the correctness of the
G\"odel-Kolmogorov translation, whose restriction to the propositional case is
due to Glivenko. This translation maps a formula $F$ of first order logic to a
formula $F^{\lnot\lnot}$ in such a way that $F$ is provable in classical logic
if and only if $F^{\lnot\lnot}$ is provable in intuitionistic logic. All formal
proofs are presented in natural deduction.
  These questions are well-known proof theoretical facts, but in textbooks,
they are often ignored or left to the reader. Because of the combinatorial
difficulty of some of the needed formal proofs, we hope that this report may be
useful, in particular to students and colleagues from other areas.

36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat