2020/07/27 by Gerald Kuba, Kuba, Gerald
Mathematics · #12F20 #54H05 #Advanced Differential Equations and Dynamical Systems #Advanced Topology and Set Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Logic (math.LO) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2007.13550
openalex publication_date 2020/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Our main result is a construction of four families C1,C2,B1,B2 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 C1vC2 contains a Cantor set. (iii) Each field in B1vB2 is a Bernstein set. (iv) All fields in C1vB1 are isomorphic. (v) If K,L are fields in C2vB2 then K is isomorphic to a subfield of L only in the trivial case K=L.