No abstract

The theorems of Steinitz concerning algebraic closure and the degree of transcendence are barred, from the algebraic point of view, by the well-ordering theorem and its theory. We wish to show how, by introducing a certain axiom on sets of sets instead of the well-ordering theorem, one is enabled to make the proofs shorter and more algebraic. The proofs will be given in terms of the non-axiomatic standpoint of set theory. DEFINITION APPLICATIONS.

No abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.

No abstract