ℵ 0 ‐Categorical Finite Extensions of Boolean Powers | Zendy

Apps A. B. | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Premium

ℵ 0 ‐Categorical Finite Extensions of Boolean Powers

Author(s) -

Apps A. B.

Publication year - 1983

Publication title -

proceedings of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.899

H-Index - 65

eISSN - 1460-244X

pISSN - 0024-6115

DOI - 10.1112/plms/s3-47.3.385

Subject(s) - mathematics , categorical variable , stone's representation theorem for boolean algebras , complete boolean algebra , two element boolean algebra , permutation (music) , boolean algebras canonically defined , automorphism , partition (number theory) , boolean ring , discrete mathematics , combinatorics , pure mathematics , algebra over a field , algebra representation , principal ideal ring , statistics , physics , commutative ring , commutative property , acoustics

We consider when a finite extension of a Boolean power of a finite perfect group by a Boolean ring R is ℵ 0 ‐categorical. We obtain necessary and sufficient conditions for this, initially in terms of a certain induced finite group of automorphisms of R , and subsequently in terms of the topological behaviour of an induced finite partition of the Stone space of R . In so doing, we introduce the notions of a ‘topological permutation system’ and a ‘Boolean representation’ thereof, and show that any topological permutation system has a unique Boolean representation, and that this representation is ℵ 0 ‐categorical. Lastly, it is shown that a subgroup of index 2 in an ℵ 0 ‐categorical group need not be ℵ 0 ‐categorical.

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research