Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The consistency of arithmetic from a point of view of constructive
  tableau method with strong negation, Part I: the system without complete
  induction   In this Part I, we shall prove the consistency of arithmetic without complete
induction from a point of view of strong negation, using its embedding to the
tableau system $\bf SN$ of constructive arithmetic with strong negation without
complete induction, for which two types of cut elimination theorems hold. One
is $\bf SN$-cut elimination theorem for the full system $\bf SN$. The other is
$\bf PCN$-cut elimination theorem for a proposed subsystem $\bf PCN$ of $\bf
SN$. The disjunction property and the E-theorem (existence property) for $\bf
SN$ are also proved. As a novelty, we shall give a simple proof of a restricted
version of $\bf SN$-cut elimination theorem as an application of the
disjunction property, using $\bf PCN$-cut elimination theorem.

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The categories of this paper are: physics
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
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The categories of this paper are: nlin