Researchers have long been interested in nding simple axiomatizations of theories, including Boolean algebra. Boolean algebra can be axiomatized in many diierent ways using various sets of operations. The ordinary operations of Boolean algebra are disjunction (+), conjunction (), negation (0), zero (0), and one (1). One of the rst simple axiomatizations was presented by E. V. (Associativity) ((...

In this paper, we shall study the algebraic structure of the set of all soft sets defined on a fixed universe. We shall show that the set of all soft sets on a fixed set of parameters is actually a Boolean algebra. Properties of the set of all soft sets on a fixed set of parameters are studied. 2010 AMS Classification: 03B52, 03G05

Partitioner algebras are defined in [2] and are natural tools for studying the properties of maximal almost disjoint families of subsets of ω. In this paper we investigate which free algebras can be represented as partitioner algebras or as subalgebras of partitioner algebras. In so doing we answer a question raised in [2] by showing that the free algebra with א1 generators is represented. It w...

If you want to cite this report, please use the following reference instead: B. De Schutter and B. De Moor, " On the sequence of consecutive powers of a matrix in a Boolean algebra, " SIAM Abstract. In this paper we consider the sequence of consecutive powers of a matrix in a Boolean algebra. We characterize the ultimate behavior of this sequence, we study the transient part of the sequence and...

This set of notes begins with a brief illustration of a few properties of Boolean logic, which may be of use to you in manipulating algebraic expressions and in identifying equivalent logic functions without resorting to truth tables. We then discuss the value of underspecifying a logic function so as to allow for selection of the simplest possible implementation. This technique must be used ca...

Stone algebras have been characterized by Chen and Grätzer in terms of triples (B;D;'), whereD is a distributive lattice with 1; B is a Boolean algebra, and ' is a bounded lattice homomorphism from B into the lattice of …lters of D: If D is bounded, the construction of these characterizing triples is much simpler, since the homomorphism ' can be replaced by one from B into D itself. The triple ...

An algebraic structure is a set with one or more operations defined on it. For example, the natural numbers with addition and multiplication are such a structure. An algebraic structure A is a Boolean algebra if it has two binary operations (∗ and +), one unary operation (∼), and two designated elements (0 and 1) such that for any x, y and z from A (x, y and z are variables whose domain is the ...

In this paper, we investigate more relations between the symmetric residuated lattices $L$ with their corresponding intuitionistic fuzzy residuated lattice $tilde{L}$. It is shown that some algebraic structures of $L$ such as Heyting algebra, Glivenko residuated lattice and strict residuated lattice are preserved for $tilde{L}$. Examples are given for those structures that do not remain the sam...