- #1
lugita15
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Omnific integers are the counterpart in the Surreal numbers of integers. The surreal numbers are usually defined using set theory, and then the omnific integers are defined as a particular subset of them. My question is, does it have to be this way? Is it possible to give a first-order axiomatization of the Omnific integers and their arithmetic, without having to define the surreal numbers themselves? I know they form a proper class, so there is a risk that they may be "too big" to describe. But Tarksi gave a first-order axiomatization for the ordinal numbers, which also form a proper class, so at least we have some hope.
Any help would be greatly appreciated.
Thank You in Advance.
Any help would be greatly appreciated.
Thank You in Advance.