It is basically the main point of the definition of ordinals that for any property of ordinals , there is a first ordinal with that property. There are, however, foundational theories without uncountable ordinals , for instance Nik Weaver’s Mathematical Conceptualism.
It is basically the main point of the definition of ordinals that for any property of ordinals , there is a first ordinal with that property. There are, however, foundational theories without uncountable ordinals , for instance Nik Weaver’s Mathematical Conceptualism.