Timeline for Archimedean completeness of some fields

6 events

when toggle format	what		by	license	comment
Apr 13, 2017 at 12:58	history	edited	CommunityBot		replaced http://mathoverflow.net/ with https://mathoverflow.net/
Nov 4, 2016 at 5:22	comment	added	Chilote		I have to admit I overlooked big part of that page. Thanks for the keen reference.
Nov 4, 2016 at 1:57	comment	added	Philip Ehrlich		@Chilote. You are mistaken. Look at the last paragraph on p. 862. It begins: "Theorem 3.2 (i.e. Hahn's Embedding Theorem) is beautifully adapted to the proof of Hahn's completeness theorem.... Hahn defines a complete ordered group to be an ordered group $G$ which does not admit a proper extension $H$ which is Archimedean relative to $G$....."
Nov 3, 2016 at 22:10	comment	added	Chilote		I understand the embedding theorem, but in the references there is not mention about the notion of Archimedean completeness. If $K$ is an archimedean extension of $\mathbb{R}((G))$, then $K$ is of type $G$ (the group of Archimedean classes of $K$ is isomorphic to $G$). Thus, by the embedding theorem there exists an embedding $\theta$ from $K$ to $\mathbb{R}((G))$. But still can happen that $K$ is a proper extension of $\mathbb{R}((G))$. How can we discard that possibility? In general, this situation is possible. For example $K((x))$ can be embedded in $K((x^2))$ being a proper extension of it
Nov 3, 2016 at 19:08	vote	accept	Chilote
Nov 3, 2016 at 14:19	history	answered	Philip Ehrlich	CC BY-SA 3.0