Simple Complete Boolean Algebras
نویسندگان
چکیده
For every regular cardinal κ there exists a simple complete Boolean algebra with κ generators.
منابع مشابه
Dually quasi-De Morgan Stone semi-Heyting algebras I. Regularity
This paper is the first of a two part series. In this paper, we first prove that the variety of dually quasi-De Morgan Stone semi-Heyting algebras of level 1 satisfies the strongly blended $lor$-De Morgan law introduced in cite{Sa12}. Then, using this result and the results of cite{Sa12}, we prove our main result which gives an explicit description of simple algebras(=subdirectly irreducibles) ...
متن کامل2 2 Ju n 20 04 SIMPLE COMPLETE BOOLEAN ALGEBRAS
For every regular cardinal κ there exists a simple complete Boolean algebra with κ generators.
متن کاملDually quasi-De Morgan Stone semi-Heyting algebras II. Regularity
This paper is the second of a two part series. In this Part, we prove, using the description of simples obtained in Part I, that the variety $mathbf{RDQDStSH_1}$ of regular dually quasi-De Morgan Stone semi-Heyting algebras of level 1 is the join of the variety generated by the twenty 3-element $mathbf{RDQDStSH_1}$-chains and the variety of dually quasi-De Morgan Boolean semi-Heyting algebras--...
متن کاملThe Completeness of the Isomorphism Relation for Countable Boolean Algebras
We show that the isomorphism relation for countable Boolean algebras is Borel complete, i.e., the isomorphism relation for arbitrary countable structures is Borel reducible to that for countable Boolean algebras. This implies that Ketonen’s classification of countable Boolean algebras is optimal in the sense that the kind of objects used for the complete invariants cannot be improved in an esse...
متن کاملFilter theory in MTL-algebras based on Uni-soft property
The notion of (Boolean) uni-soft filters in MTL-algebras is introduced, and several properties of them are investigated. Characterizations of (Boolean) uni-soft filters are discussed, and some (necessary and sufficient) conditions for a uni-soft filter to be Boolean are provided. The condensational property for a Boolean uni-soft filter is established.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1974