This is the personal website of Jason Zhang.
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There have been a great deal of study concerning ordinals and their properties. However, there have not been as much studies based on the order reversal (or dual) of these ordinals, and specifically if these can be extended into uncountable variations or analogues. Several different extensions are analyzed and evaluated based on how they reflect \(\omega_{1}\). The three main candidates are the reversal of the first uncountable ordinal, a branching tree-like partial order of the reversed countable ordinals, and the product of different order types. After considering various properties of these candidates such as initial segments, cofinality, and potential use cases, the best extension was determined to be the reversal of the first uncountable ordinal.
Will post preprint later.
Set Theory, Order Theory