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A characterization of the meager ideal

Piotr Zakrzewski (2015)

Commentationes Mathematicae Universitatis Carolinae

We give a classical proof of the theorem stating that the σ -ideal of meager sets is the unique σ -ideal on a Polish group, generated by closed sets which is invariant under translations and ergodic.

A characterization of tribes with respect to the Łukasiewicz t -norm

Erich Peter Klement, Mirko Navara (1997)

Czechoslovak Mathematical Journal

We give a complete characterization of tribes with respect to the Łukasiewicz t -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 t -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 t -norms, e. g., for the product t -norm.

A characterization of uninorms on bounded lattices via closure and interior operators

Gül Deniz Çayli (2023)

Kybernetika

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 classification of ordinals up to Borel isomorphism

Su Gao, Steve Jackson, Vincent Kieftenbeld (2008)

Fundamenta Mathematicae

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.

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