Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Retracts of Posets: The Chain_gap Property and the Selection Property
  are Independant   Posets which are retract of products of chains are characterized by means of
two properties: \emph{the chain-gap property} and \emph{the selection property}
(Rival and Wille, 1981 \cite {R-W}). Examples of posets with the selection
property and not the chain-gap property are easy to find. To date, the Boolean
lattice $\Power (\omega_1)/Fin$ was the sole example of lattice without the
selection property \cite {R-W}. We prove that it does not have the chain-gap
property. We provide an example of a lattice which has the chain-gap property
but not the selection property. This answer questions raised in \cite {R-W}.

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The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys