Non-separable Banach spaces with non-meager Hamel basis
We show that an infinite-dimensional complete linear space X has: ∙ a dense hereditarily Baire Hamel basis if |X| ≤ ⁺; ∙ a dense non-meager Hamel basis if for some cardinal κ.
Nonstandard arithmetic of function fields over H-convex subfields of *Q.
Nonstandard hulls of locally uniform groups
We present a nonstandard hull construction for locally uniform groups in a spirit similar to Luxemburg's construction of the nonstandard hull of a uniform space. Our nonstandard hull is a local group rather than a global group. We investigate how this construction varies as one changes the family of pseudometrics used to construct the hull. We use the nonstandard hull construction to give a nonstandard characterization of Enflo's notion of groups that are uniformly free from small subgroups. We...
Nonstandard implication algebras
Nonstandard implication algebras
Nonstandard Integration Theory in Topological Vector Lattices.
Nonstandard models of arithmetic as an alternative basis for continuum considerations
Non-stochastic uncertainty quantification of a multi-model response
The focus is put on the application of fuzzy sets and Dempster-Shafer theory in assessing the nature and extent of uncertainty in the response of models that model the same phenomenon and depend on fuzzy input data. Dempster-Shafer theory uses a weighted family of fixed sets called the focal elements to evaluate the relationship between an arbitrarily chosen set and the focal elements. It is proposed to create at least weighted focal elements on the basis of 1) the responses to fuzzy inputs...
Normal Form Theorem for Systems of Sequents
Normal forms in partial modal logic
A "partial" generalization of Fine's definition [Fin] of normal forms in normal minimal modal logic is given. This means quick access to complete axiomatizations and decidability proofs for partial modal logic [Thi].
Normal forms in the typed -calculus with tuple types
Normal numbers and subsets of N with given densities
For X ⊆ [0,1], let denote the collection of subsets of ℕ whose densities lie in X. Given the exact location of X in the Borel or difference hierarchy, we exhibit the exact location of . For α ≥ 3, X is properly iff is properly . We also show that for every nonempty set X ⊆[0,1], is -hard. For each nonempty set X ⊆ [0,1], in particular for X = x, is -complete. For each n ≥ 2, the collection of real numbers that are normal or simply normal to base n is -complete. Moreover, , the...
Normal numbers and the Borel hierarchy
We show that the set of absolutely normal numbers is Π⁰₃-complete in the Borel hierarchy of subsets of real numbers. Similarly, the set of absolutely normal numbers is Π⁰₃-complete in the effective Borel hierarchy.
Normal restrictions of the noncofinal ideal on
We discuss the problem of whether there exists a restriction of the noncofinal ideal on that is normal.
Normal Subgroup of Product of Groups
In [6] it was formalized that the direct product of a family of groups gives a new group. In this article, we formalize that for all j ∈ I, the group G = Πi∈IGi has a normal subgroup isomorphic to Gj. Moreover, we show some relations between a family of groups and its direct product.
Normalisation of the theory of Cartesian closed categories and conservativity of extensions of
Normalisation of the Theory T of Cartesian Closed Categories and Conservativity of Extensions T[x] of T
Using an inductive definition of normal terms of the theory of Cartesian Closed Categories with a given graph of distinguished morphisms, we give a reduction free proof of the decidability of this theory. This inductive definition enables us to show via functional completeness that extensions of such a theory by new constants (“indeterminates”) are conservative.
Normality and Martin's axiom
Normalization as a consequence of cut elimination
Norms on possibilities. II: More ccc ideals on .