Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reverse Mathematics and initial intervals   In this paper we study the reverse mathematics of two theorems by Bonnet
about partial orders. These results concern the structure and cardinality of
the collection of the initial intervals. The first theorem states that a
partial order has no infinite antichains if and only if its initial intervals
are finite unions of ideals. The second one asserts that a countable partial
order is scattered and does not contain infinite antichains if and only if it
has countably many initial intervals. We show that the left to right directions
of these theorems are equivalent to ACA_0 and ATR_0, respectively. On the other
hand, the opposite directions are both provable in WKL_0, but not in RCA_0. We
also prove the equivalence with ACA_0 of the following result of Erd\"os and
Tarski: a partial order with no infinite strong antichains has no arbitrarily
large finite strong antichains.

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The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int