An Alternative Proof of the Well-Foundedness of the Nested Multiset Ordering
نویسنده
چکیده
This research note outlines an alternative proof of the well-foundedness of the nested multiset ordering. It is first shown that the set M∗(S) of nested multisets over a given base set S forms a cumulative type structure. Then, by exploiting the notion of sets bounded in rank, it is proved that (M∗(S), >>∗) is well-founded if and only if (S, >) is well-founded, where >>∗denotes a nested multiset ordering on M∗(S) and > is an ordering on S. Mathematics Subject Classification: 03B05, 00A30 MSC: 03B05, 00A30
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