Properties of Wqos
- Given a quasiordering the quasiordering defined by is well-founded if and only if is a wqo.
- A quasiordering is a wqo if and only if the corresponding partial order (obtained by quotienting by ) has no infinite descending sequences or antichains. (This can be proved using a Ramsey argument as above)
Read more about this topic: Well-quasi-ordering
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“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)