English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Introduction. In the theory of 7la-sets three main theorems stand out: I. An 77-set is universal for totally ordered sets of power not exceeding Ka. II. Two 71a-sets of power R. are isomorphic. III. If R. is regular and if Ea 0 then these three theorems hold for the category of totally ordered Abelian groups and order preserving (group) isomorphisms; the special group being totally ordered, Abelian, divisible, and an 77a-set. Erdos, Gillman, and Henriksen [8] (see also Gillman and Jerison [11]) proved that if a> 0 then I and II hold for the category of totally ordered fields and order preserving (ring) isomorphisms; the special field being real-closed and an 7a-set. It was also shown in [8] that III holds for this category and special object if a = 1. However in case a > 1, III was left open both in [8] and in [11]. The initial aim of these researches was to show that, assuming a> 0, K, regular, and Ea 0. Let R { G } denote the field of formal power series with exponents in G and coefficients in R, the reals. R{G } is an 7la-set but its power exceeds K. Let R { G } a = {f ER { G }: the support of f is of power less than a }. Then R{G } a, again a real-closed field, is an 77a-set, and is of power K,. The only difficult point in these verifications was the proof that R { G } and R{G}a are 77a-sets. The proof arrived at by the author did not involve the multiplication in these fields, but depended wholly on their structure as a

On the existence of real-closed fields that are $\eta \sb{\alpha }$-sets of power $\aleph \sb{\alpha }$