A characterization of internal sets
A characterization of lifting generics for Sacks-like forcings
A characterization of polarities whose lattice of polars is Boolean
A characterization of quantic quantifiers in orthomodular lattices.
A characterization of quasivarieties of partial algebras by means of limits and products.
A characterization of r-maximal sets.
A characterization of Takeuti's ordinal diagrams of finite order.
A characterization of the meager ideal
We give a classical proof of the theorem stating that the -ideal of meager sets is the unique -ideal on a Polish group, generated by closed sets which is invariant under translations and ergodic.
A Characterization of the Veblen-Schütte Functions by Means of Functionals
A characterization of tribes with respect to the Łukasiewicz -norm
We give a complete characterization of tribes with respect to the Łukasiewicz -norm, i. e., of systems of fuzzy sets which are closed with respect to the complement of fuzzy sets and with respect to countably many applications of the Łukasiewicz -norm. We also characterize all operations with respect to which all such tribes are closed. This generalizes the characterizations obtained so far for other fundamental -norms, e. g., for the product -norm.
A characterization of uninorms on bounded lattices via closure and interior operators
Uninorms on bounded lattices have been recently a remarkable field of inquiry. In the present study, we introduce two novel construction approaches for uninorms on bounded lattices with a neutral element, where some necessary and sufficient conditions are required. These constructions exploit a t-norm and a closure operator, or a t-conorm and an interior operator on a bounded lattice. Some illustrative examples are also included to help comprehend the newly added classes of uninorms.
A characterization of well-orders
A class of -preduals which are isomorphic to quotients of
For every countable ordinal α, we construct an -predual which is isometric to a subspace of and isomorphic to a quotient of . However, is not isomorphic to a subspace of .
A class of sets whose distance set fills an interval
A classification of an iterative hierarchy.
A classification of definable forcings on ω1
Under the assumption of the existence of sharps for reals all simply definable posets on are classified up to forcing equivalence.
A classification of ordinals up to Borel isomorphism
We consider the Borel structures on ordinals generated by their order topologies and provide a complete classification of all ordinals up to Borel isomorphism in ZFC. We also consider the same classification problem in the context of AD and give a partial answer for ordinals ≤ω₂.
A classification of separable Rosenthal compacta and its applications [Book]
A classification of the one-argument primitive recursive functions.
A classification of the ordinal recursive functions.