Talk:Ordered exponential field/Archive 1

The condition that 1/n < E(1) < n

This condition, appearing in the definition in the first sentence of the article, is completely ignored for the rest of the article. This makes it completely mysterious. Why should this condition be part of the definition? What kinds of ordered exponential fields satisfy the rest of the definition without this condition? Do the model-theoretic results described later in the article depend on this condition? This is not my area, and I can't answer these questions. Someone who knows something should address this in the article. — Preceding unsigned comment added by 2601:18C:4302:3140:850B:AE1A:B680:25B6 (talk) 19:52, 6 January 2018 (UTC)

The definition of an exponentially closed field used in this page is due to Alling's work in the 1960s. By now it is known that any ordered field that admits an order-preserving isomorphism from its ordered additive group to its ordered multiplicative group of positive elements also admits such an isomorphism with the property under discussion (see Lemma 1.17 of S. Kuhlmann, "Ordered Exponential Fields", Fields Institute Monographs 12, 2000). Since Kuhlmann's work is more recent and, to my knowledge, the most extensive work on ordered exponential fields, I suggest that the notions and terminology of this monograph are used for the definitions. I will try to write the page on ordered exponential fields in the next few days and combine it with this article. LSKDuck (talk) 09:34, 20 April 2019 (UTC)

I have written an article on ordered exponential fields, which is currently under review and retrievable in my Sandbox. Further explanation can be found here. LSKDuck (talk) 18:35, 21 April 2019 (UTC)