Fine Analysis of the Quasi-Orderings on the Power Set |
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Authors: | Alberto Marcone |
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Institution: | (1) Dipartimento di Matematica e Informatica, Università di Udine, viale delle Scienze 206, 33100 Udine, Italy |
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Abstract: | We pursue the fine analysis of the quasi-orderings ![prcue](/content/bv7xl4hwjuhqujvq/xxlarge8828.gif)
and ![prcue](/content/bv7xl4hwjuhqujvq/xxlarge8828.gif)
on the power set of a quasi-ordering (Q, ). We set X![prcue](/content/bv7xl4hwjuhqujvq/xxlarge8828.gif)
Y if every x X is majorized in by some y Y, and X![prcue](/content/bv7xl4hwjuhqujvq/xxlarge8828.gif)
Y if every y Y is minorized in by some x X. We show that both these quasi-orderings are -wqo if and only if the original quasi-ordering is ( )-wqo. For ![prcue](/content/bv7xl4hwjuhqujvq/xxlarge8828.gif)
this holds also restricted to finite subsets, thus providing an example of a finitary operation on quasi-orderings which does not preserve wqo but preserves bqo. |
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Keywords: | well quasi-ordering better quasi-ordering -wqo" target="_blank">gif" alt="agr" align="BASELINE" BORDER="0">-wqo |
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