Automorphisms of Medial Fields

✍ Scribed by John L. Hickman

• Publisher: John Wiley and Sons
• Year: 1982
• Tongue: English
• Weight: 371 KB
• Volume: 28
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.19820281410

✦ Synopsis

We recall from [l] that medial fields can exist in certain models of ZERMELO-FR~ESKEL set theory, and that if F is a medial field, then .F can be represented as the direct limit of a strictly increasing m-sequence (9n)lL<w of finite subfields. If we let 11 be the (necessarily nonzero) characteristic of g, then for each n FIX will have p"'n elements for some natural number m,. Thus we can associate with a sequence (m,,),,,,, which we shall call a "pseudo-type'' of 9. Clearly 9 can be represented as a direct limit of finite fields in more than one way, and thus has more than one pseudo-type. We let the set of all pseudo-types of 9 be denoted by " P T ( F ) " , and 11 e adopt the convention that whenever we make use of a specific pseudo-type

( n ~~, ) , ~< ~.

then 'no = 1.

Let .F. 2 be two medial fields. M'e say that 9 and 2 are equivalent and write .F = A