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math.LO2015★ 6 cited
Ordered Fields, the Purge of Infinitesimals from Mathematics and the Rigorousness of Infinitesimal Calculus
James F. Hall, Todor D. Todorov
We present a characterization of the completeness of the field of real numbers in the form of a \emph{collection of several equivalent statements} borrowed from algebra, real analy…
math.LO2011★ 7 cited
Completeness of Ordered Fields
James Forsythe Hall
The main goal of this project is to prove the equivalency of several characterizations of completeness of Archimedean ordered fields; some of which appear in most modern literature…
math.LO2011
Another Proof of the Existence a Dedekind Complete Totally Ordered Field
James F. Hall, Todor D. Todorov
We describe the Dedekind cuts explicitly in terms of non-standard rational numbers. This leads to another construction of a Dedekind complete totally ordered field or, equivalently…