Cantor sets and fields of reals
Commutative Algebra
2022-01-24 v2 Logic
Abstract
Our main result is a construction of four families C_1,C_2,B_1,B_2 which are equipollent with the power set of the real line R and satisfy the following properties. (i) The members of the families are proper subfields of R whose algebraic closures equal the field C. (ii) Each field in C_1vC_2 contains a Cantor set. (iii) Each field in B_1vB_2 is a Bernstein set. (iv) All fields in C_1vB_1 are isomorphic. (v) If K,L are fields in C_2vB_2 then K is isomorphic to a subfield of L only in the trivial case K=L.
Cite
@article{arxiv.2007.13550,
title = {Cantor sets and fields of reals},
author = {Gerald Kuba},
journal= {arXiv preprint arXiv:2007.13550},
year = {2022}
}