Sentence examples for Positive formula from inspiring English sources

Ted Weisberg, a floor trader at Seaport Securities, said: "Clearly, clearly, a democratic Congress and a democratic president is not necessarily a positive formula for the stockmarket, and when you combine that with all the potential changes we might have to take into account and look at, and when you combine that with a weak US economy, weak corporate profits, it could be problematic".

We briefly review the paradoxes: the Russell paradox doesn't work because x ∉ x is not a positive formula; notice that {x | x ∈ x} exists!

A generalized positive formula is obtained if we allow bounded universal and existential quantifications (the additional strength comes from allowing (∀x ∈ A | φ) ≡ ∀x(x ∈ A → φ); bounded existential quantification is positive in any case).

A positive formula is a formula which belongs to the smallest class of formulas containing a false statement ⊥, all atomic membership and equality formulas and closed under the formation of conjunctions, disjunctions, universal and existential quantifications.

It is also not too hard to show that if all typed versions of a generalized positive formula φ in the language of the intended model (with sequences s appearing as values of free variables replaced by their values at the appropriate types) are true, then the original formula φ is true in the intended model.

Positive comprehension is motivated superficially by an attack on one of the elements of Russell's paradox (the negation): a positive set theory will be expected to support the axiom of extensionality (as usual) and the axiom of (generalized) positive comprehension: for any (generalized) positive formula φ, {x | φ} exists.

Four positive formulae for type A quiver polynomials (with Ezra Miller and Mark Shimozono), Inventiones Mathematicae 166 (2006), no. 2. Gröbner geometry of Schubert polynomials (with Ezra Miller), Annals of Mathematics 161 (2005), 1245 1318.

Moreover we clarify that Lifschitz's pointwise circumscription is complete in a slightly wider class of positive formulas.

If the unrestricted comprehension principle is similarly restricted to the positive formulae, we also get a consistent theory.

We mention that we are aware that positive comprehension with the additional generalization of positive formulas allowing one to include set abstracts {x | φ} (with φ generalized positive) in generalized positive formulas is consistent, but turns out not to be consistent with extensionality.

Note that although we only stipulate the density be positive, the formula (68) must be applied to all conserved variables (uinboldsymbol{U}).