ar X iv : 0 80 9 . 05 38 v 1 [ m at h . L O ] 3 S ep 2 00 8 BOOLEAN ALGEBRAS AND LOGIC
نویسنده
چکیده
In this article we investigate the notion and basic properties of Boolean algebras and prove the Stone’s representation theorem. The relations of Boolean algebras to logic and to set theory will be studied and, in particular, a neat proof of completeness theorem in propositional logic will be given using Stone’s theorem from Boolean algebra. We mention here that the method we used can also be extended to first order logic, yet we will not go for it in this paper.
منابع مشابه
ar X iv : m at h / 05 08 44 5 v 1 [ m at h . L O ] 2 4 A ug 2 00 5 INVARIANT MEASURES IN LUKASIEWICZ LOGIC
We prove that on the finitely generated free MV-algebras the only automorphism-invariant truth averaging process that detects pseudotrue propositions is the integral with respect to Lebesgue measure.
متن کاملar X iv : h ep - t h / 03 12 24 0 v 1 1 9 D ec 2 00 3 New realizations of observables in dynamical systems with second class constraints
New realizations of observables in dynamical systems with second class constraints. Abstract In the Dirac bracket approach to dynamical systems with second class constrains the observables are represented by elements of a quotient Dirac bracket algebra. We describe the constraints which allow to construct families of new realizations of this algebra. The realizations are obtained as quotients o...
متن کاملMonadic Bounded Commutative Residuated l-monoids
An algebra M = (M ; ,∨,∧,→, 0, 1) of type 〈2, 2, 2, 2, 0, 0〉 is called a bounded commutative R`-monoid iff (i) (M ; , 1) is a commutative monoid, (ii) (M ;∨,∧, 0, 1) is a bounded lattice, and (iii) x y ≤ z ⇐⇒ x ≤ y → z, (iv) x (x → y) = x ∧ y, for each x, y, z ∈ M . In the sequel, by an R`-monoid we will mean a bounded commutative R`-monoid. (Note that bounded commutative R`-monoids are just bo...
متن کاملRelation Algebras for Reasoning about Time and Space
This paper presents a brief introduction to relation algebras, including some examples motivated by work in computer science, namely, the ‘interval algebras’, relation algebras that arose from James Allen’s work on temporal reasoning, and by ‘compass algebras’, which are designed for similar reasoning about space. One kind of reasoning problem, called a ‘constraint satisfaction problem’, can be...
متن کاملar X iv : m at h / 05 11 38 2 v 2 [ m at h . R T ] 1 9 Ju n 20 06 Equivalences between cluster categories ∗
Tilting theory in cluster categories of hereditary algebras has been developed in [BMRRT] and [BMR]. Some of them are already proved for hereditary abelian categories there. In the present paper, all basic results about tilting theory are generalized to cluster categories of hereditary abelian categories. Furthermore, for any tilting object T in a hereditary abelian category H, we verify that t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008