Results 141 to 150 of about 296,040 (177)
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Mathematical Logic Quarterly, 1992
AbstractIn 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 algebra freely generated by a set.
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AbstractIn 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 algebra freely generated by a set.
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Algebraic partial Boolean algebras
Journal of Physics A: Mathematical and General, 2003Partial Boolean algebras are algebraic in this paper in the sense that their elements have coordinates in an algebraic number field. Within this context the author shows that every algebraic finitely-generated partial Boolean algebra is finite when the underlying space is three-dimensional.
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Mathematics of the USSR-Sbornik, 1973
The paper contains the construction of a general theory of Boolean-valued algebras: There are introduced the notions of a homeomorphism, congruence, subalgebra and direct product. It is shown that these algebras possess properties that are totally analogous to the properties of two-valued algebras.
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The paper contains the construction of a general theory of Boolean-valued algebras: There are introduced the notions of a homeomorphism, congruence, subalgebra and direct product. It is shown that these algebras possess properties that are totally analogous to the properties of two-valued algebras.
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Postulates for Boolean Algebras
Canadian Journal of Mathematics, 1953The independence of postulates for well-known systems is a question of general interest. A closely related question is whether or not, by altering one or more of the postulates in an independent set, the set remains independent.
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Journal of Symbolic Logic, 2000
Feiner [F] showed that a Boolean algebra need not have a computable copy (see also [T2]). Downey and Jockusch [D-J] showed that every low Boolean algebra does have a computable copy. Thurber [T3], showed that every low2 Boolean algebra has a computable copy. Here we show that every Boolean algebra which is low3, or even low4, has a computable copy.The
Julia F. Knight, Michael Stob
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Feiner [F] showed that a Boolean algebra need not have a computable copy (see also [T2]). Downey and Jockusch [D-J] showed that every low Boolean algebra does have a computable copy. Thurber [T3], showed that every low2 Boolean algebra has a computable copy. Here we show that every Boolean algebra which is low3, or even low4, has a computable copy.The
Julia F. Knight, Michael Stob
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Acta Mathematica Sinica, English Series, 2004
Let \(X\) be a Banach space. The classical Orlicz-Pettis theorem says that weak subseries convergence already implies subseries convergence. The authors use the term \(P(\mathbb N)\) is \(X\)-weakly summing to express that the conclusion of the Orlicz-Pettis theorem holds in \(X\) when subseries corresponding to all subsets of \(\mathbb N\) are ...
Aizpuru, Antonio +1 more
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Let \(X\) be a Banach space. The classical Orlicz-Pettis theorem says that weak subseries convergence already implies subseries convergence. The authors use the term \(P(\mathbb N)\) is \(X\)-weakly summing to express that the conclusion of the Orlicz-Pettis theorem holds in \(X\) when subseries corresponding to all subsets of \(\mathbb N\) are ...
Aizpuru, Antonio +1 more
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A Representation for Boolean Algebras
American Journal of Mathematics, 19511. The content. The success of Stone [5] in representing Boolean algebras by fields of sets leads one to search for other representations. (See also [2, p. 159], [4].) Using splitting endomorphisms on a type of Abelian group with an order relation, we are led to a faithful representation of a given Boolean algebra B. The group employed will be called a
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On the Representation of Boolean Algebras
Canadian Mathematical Bulletin, 1962Let B be a Boolean algebra and let ℳ and n be two systems of subsets of B, both containing all finite subsets of B. Let us assume further that the join ∨M of every set M∊ℳ and the meet ∧N of every set N∊n exist.
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HYPERIDENTITIES OF BOOLEAN ALGEBRAS
Russian Academy of Sciences. Izvestiya Mathematics, 1993See the review in Zbl 0773.08003.
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Canadian Journal of Mathematics, 1971
A Boolean algebra B is a retract of an algebra A if there exist homomorphisms ƒ: B → A and g: A → B such that gƒ is the identity map B. Some important properties of retracts of Boolean algebras are stated in [3, §§ 30, 31, 32]. If A and B are a-complete, and A is α-generated by B, Dwinger [1, p.
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A Boolean algebra B is a retract of an algebra A if there exist homomorphisms ƒ: B → A and g: A → B such that gƒ is the identity map B. Some important properties of retracts of Boolean algebras are stated in [3, §§ 30, 31, 32]. If A and B are a-complete, and A is α-generated by B, Dwinger [1, p.
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