# Slender classes

## Related Articles

- Realization of Boolean functions by repetition-free formulas in a particular base. Sharankhaev, I. K. // Siberian Mathematical Journal;Jan2009, Vol. 50 Issue 1, p188
Under study are the representations of Boolean functions by formulas. We offer a criterion for the Boolean functions to be repetition-free in the base {V,Â·, âˆ’0, 1, x1( x2 V x3 x4) V x5( x3 V x2 x4)}.

- Peirce Algebras and Boolean Modules. Hirsch, R. // Journal of Logic & Computation;Apr2007, Vol. 17 Issue 2, p255
A boolean module comprises a relation algebra, a boolean algebra and a Peircean operator which must obey a certain finite set of equational axioms. A Peirce algebra is a boolean module with one more operator, right cylindrification, which must obey another finite set of equational axioms. A...

- On ultraproducts of Boolean algebras and irr. Shelah, Saharon // Archive for Mathematical Logic;Aug2003, Vol. 42 Issue 6, p569
1. Consistent inequality [We prove the consistency of irr(Î B[subi]/D) < Î irr(B[subi])/D where D is an ultrafilter on K and each B[subi] is a Boolean algebra and irr(B) is the maximal size of irredundant subsets of a Boolean algebra B, see full definition in the text. This solves the last...

- Representation of C-Algebras by Sections of Sheaves. Swamy, U. M.; Rao, G. C.; Kumar, R. V. G. Ravi // Southeast Asian Bulletin of Mathematics;2004, Vol. 28 Issue 6, p1121
In this paper, we prove that every C-algebra with T is isomorphic to the C-algebra of all global sections of a sheaf of indecomposable C-algebras over a Boolean space and that every sheaf of indecomposable C-algebras with T over a Boolean space is isomorphic to the sheaf obtained from the...

- Dense Elements in Almost Distributive Lattices. Rao, G. C.; Rao, G. Nanaji // Southeast Asian Bulletin of Mathematics;2004, Vol. 27 Issue 6, p1081
The properties of the set D of dense elements of an ADL is studied. The filter congruence Î¸D generated by D in *-ADLs are characterized. *-ADLs are characterized in terms of dense elements. A necessary and sufficient condition for a *-ADLs to become a Boolean algebra is established.

- BoolÂ·eÂ·an algebra. // American Heritage Student Science Dictionary;2009, p46
A definition of the term "Boolean algebra" is presented. It refers to a mathematical system dealing with the relationship between sets, used to solve problems in logic and engineering. Variables consist of 0 and 1 and operations are expressed as AND, OR, and NOT. Boolean algebra has been...

- Normal and complete Boolean ambiguity algebras and MV-pairs1. de la Vega, Hernán // Logic Journal of the IGPL;Dec2012, Vol. 20 Issue 6, p1133
In 2006, both Gejza JenÄa and Thomas Vetterlein, building on different hypotheses, represented MV-algebras through the quotient of a Boolean algebra B by a subgroup of the group of all automorphisms of B. It is shown in this article that Vetterlein's constructions are particular cases of...

- Cryptographic Boolean Functions with R. Lafitte, Frédéric; van Heule, Dirk; van hamme, Julien // R Journal;Jun2011, Vol. 3 Issue 1, p44
Anew package called boolfun is available for R users. The package provides tools to handle Boolean functions, in particular for cryptographic purposes. This document guides the user through some (code) examples and gives a feel of what can be done with the package.

- Symmetric Propositions and Logical Quantifiers. Taylor, R. // Journal of Philosophical Logic;Dec2008, Vol. 37 Issue 6, p575
Symmetric propositions over domain $\mathfrak{D}$ and signature $\Sigma = \langle R^{n_1}_1, \ldots, R^{n_p}_p \rangle$ are characterized following Zermelo, and a correlation of such propositions with logical type- $\langle \vec{n} \rangle$ quantifiers over $\mathfrak{D}$ is described. Boolean...