We prove an uncertainty principle for certain eigenfunction expansions on L2(R+,w(r)dr) and use it to analogues of theorems Chernoff Ingham Laplace-Beltrami operators compact symmetric spaces, special Hermite operator Cn Rn.

Probability theory and fuzzy logic have been presented as quite distinct theoretical foundations for reasoning and decision making in situations of uncertainty. This paper establishes a common basis for both forms of logic of uncertainty in which a basic uncertainty logic is defined in terms of a valuation on a lattice of propositions. The (non-truth-functional) connectives for conjunction, dis...

♣ Rings . A ring is a non-empty set R with two binary operations ( + , · ) , called addition and multiplication, respectively satisfying : Axiom 1. Closure ( + ) : ∀x, y ∈ R , x + y ∈ R . Axiom 2. Commutative ( + ) : For every x, y ∈ R , x + y = y + x . Axiom 3. Associative ( + ) : ∀x, y, z ∈ R , x + (y + z) = (x + y) + z . Axiom 4. Neutral ( + ) : ∃ θ ∈ R , such that ∀x ∈ R, x + θ = θ + x = x ...

The following notion of forcing was introduced by Grigorieff [2]: Let I ⊂ ω be an ideal, then P is the set of all functions p : ω → 2 such that dom(p) ∈ I. The usual Cohen forcing corresponds to the case when I is the ideal of finite subsets of ω. In [2] Grigorieff proves that if I is the dual of a p-point ultrafilter, then ω1 is preserved in the generic extension. Later, when Shelah introduced...

A new axiom is proposed, the Ground Axiom, asserting that the universe is not a nontrivial set forcing extension of any inner model. The Ground Axiom is first-order expressible, and any model of zfc has a class forcing extension which satisfies it. The Ground Axiom is independent of many well-known set-theoretic assertions including the Generalized Continuum Hypothesis, the assertion v=hod that...