And the set of all functions from set X to set Y can be understood as the particular case Set (X, Y) of this convention where C is taken to be the class Set of all sets, which we can think of as discrete algebras, that is, algebras with no structure. ❋ Pratt, Vaughan (2007)
Boolean algebras, which is the algebraic semantics for classical logic, and the class HA of Heyting algebras, which is the algebraic semantics for intuitionistic logic. ❋ Jansana, Ramon (2006)
L-algebras is a class of L-algebras which is the class of all the models of some set of L-equations. ❋ Jansana, Ramon (2006)
A quasivariety of L-algebras is a class of algebras which is the class of the models of some set of ❋ Jansana, Ramon (2006)
His geometric interests extended to Clifford algebras these describe geometrical structures in a compact way and have wide applications in physics and in computer vision and he published a standard work on the subject in 1995. ❋ Unknown (2011)
My wife Emiko Nakayama's father, Tadasi, was a mathematician known for his research on Frobenius algebras. ❋ Unknown (2009)
The study of Boolean algebras has several aspects: structure theory, model theory of Boolean algebras, decidability and undecidability questions for the class of Boolean algebras, and the indicated applications. ❋ Monk, J. Donald (2009)
Not long after this he discovered a translation between Boolean algebras and Boolean rings; under this translation the ideals of a Boolean algebra corresponded precisely to the ideals of the associated Boolean ring. ❋ Burris, Stanley (2009)
In hindsight these theorems (which explicitly concern boolean algebras, of course) can be viewed as in effect a treatment of all the basic modal axioms and corresponding properties of the accessibility relation. ❋ Unknown (2009)
His next major contribution was to establish a correspondence between Boolean algebras and certain topological spaces now called Boolean spaces (or Stone spaces). ❋ Burris, Stanley (2009)
This study helped mathematicians to recognise an aspect of the wide variety of algebras which could be examined; it also played a role in the development of model theory in the U.S. in the early 1900s. ❋ Unknown (2009)
In the 1930s Garrett Birkhoff established the fundamental results of equational logic, namely (1) equational classes of algebras are precisely the classes closed under homomorphisms, subalgebras and direct products, and (2) equational logic is based on five rules: reflexivity, symmetry, transitivity, replacement, and substitution. ❋ Burris, Stanley (2009)
Structure theory and cardinal functions on Boolean algebras ❋ Monk, J. Donald (2009)
This led to questions paralleling those already posed and resolved for Boolean algebras, for example, was every model of his axioms for relation algebras isomorphic to an algebra of relations on a set? ❋ Burris, Stanley (2009)
(Lindenbaum-Tarski algebras and model theory), set theory (fields of sets), topology (totally disconnected compact Hausdorff spaces), foundations of set theory (Boolean-valued models), measure theory ❋ Monk, J. Donald (2009)
However, if in relation algebras (the calculus of relations) one wants to formalize a set theory which has something such as the pair axiom, then one can reduce many variables to three variables, and so it is possible to express any first-order statement of such a theory by an equation. ❋ Burris, Stanley (2009)
Boolean algebra is the algebra of two-valued logic with only sentential connectives, or equivalently of algebras of sets under union and complementation. ❋ Monk, J. Donald (2009)
These two processes are inverses of one another, and show that the theory of Boolean algebras and of rings with identity in which every element is idempotent are definitionally equivalent. ❋ Monk, J. Donald (2009)
Her own research (with Brauer and Hasse) in 1930 solved a famous problem in the theory of algebras. ❋ Unknown (2009)
In addition, although not explained here, there are connections to other logics, subsumption as a part of special kinds of algebraic logic, finite Boolean algebras and switching circuit theory, and Boolean matrices. ❋ Monk, J. Donald (2009)
