Boolean powers over incomplete boolean algebras

Boolean Powers in Algebraic Logic

✍ Aubert Daigneault 📂 Article 📅 1971 🏛 John Wiley and Sons 🌐 English ⚖ 683 KB

Closure Algebras and Boolean Algebras

✍ G. J. Logan 📂 Article 📅 1977 🏛 John Wiley and Sons 🌐 English ⚖ 212 KB

## S(z A y ) z S(A), by (c) * S(z) A S(Y) 2 S(A) e S(x) 2 S(A) and S(y) 2 S(A) e C ( s ) s C ( A ) 'and C ( y ) E C ( A ) , by (c) o x € C ( A ) and Y E C ( A ) . Now every ultrafilter is consistent and closed with respect to C, since if U is an ultrafilter and C ( U ) = X , then C({,uu,, . . ., ,

σ-short Boolean algebras

✍ Makoto Takahashi; Yasuo Yoshinobu 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 145 KB

## Abstract We introduce properties of Boolean algebras which are closely related to the existence of winning strategies in the Banach‐Mazur Boolean game. A __σ__‐short Boolean algebra is a Boolean algebra that has a dense subset in which every strictly descending sequence of length __ω__ does not

BOOLEAN ALGEBRAS IN AST

✍ Klaus Schumacher 📂 Article 📅 1992 🏛 John Wiley and Sons 🌐 English ⚖ 489 KB

## Abstract In this paper we investigate Boolean algebras and their subalgebras in Alternative Set Theory (AST). We show that any two countable atomless Boolean algebras are isomorphic and we give an example of such a Boolean algebra. One other main result is, that there is an infinite Boolean alge

Boolean Products of BL-Algebras

✍ Antonio Di Nola; George Georgescu; Laurenţiu Leuştean 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 188 KB

The representation of algebras by Boolean products is a very general problem in universal algebra. In this paper we shall characterize the Boolean products of BL-chains, the weak Boolean products of local BL-algebras, and the weak Boolean products of perfect BL-algebras.

Special subalgebras of Boolean algebras

✍ J. Donald Monk 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 141 KB

We consider eight special kinds of subalgebras of Boolean algebras. In Section 1 we describe the relationships between these subalgebra notions. In succeeding sections we consider how the subalgebra notions behave with respect to the most common cardinal functions on Boolean algebras.