I intend not to or atleast the sense is meant to be compatible with the mathematical word. Looking at wikipedia article for “Field” subsection “ordered fields” there is the mention that real are the unique complete field up to isomorphism and there are multiple subsections in surreals that could contend to be isomorphic. Real multiples of w also have an additive inverse and multiplicative inverse making them “another copy” of the reals. I think I might have thougt in error that the other subsection would fullfill field axioms in its own right but rather it is just a subsection that can be mapped to reals.
I intend not to or atleast the sense is meant to be compatible with the mathematical word. Looking at wikipedia article for “Field” subsection “ordered fields” there is the mention that real are the unique complete field up to isomorphism and there are multiple subsections in surreals that could contend to be isomorphic. Real multiples of w also have an additive inverse and multiplicative inverse making them “another copy” of the reals. I think I might have thougt in error that the other subsection would fullfill field axioms in its own right but rather it is just a subsection that can be mapped to reals.