We consider the tropicalization of tangent lines to a complete intersection curveXXin<inline-formula alttext="double-struck upper P Superscri...

In category theory, most set-theoretic constructions—union, intersection, etc.—have direct categorical counterparts. But up to now, there is no direct construction of a deletion operation like the set-theoretic complement. In rule-based transformation systems, deletion of parts of a given object is one of the main tasks. In the double pushout approach to algebraic graph transformation, the cons...

in this paper, we construct two fuzzy sets using the notions of level subsets and strong level subsets of a given fuzzy set in a ring r. these fuzzy sets turn out to be identical and provide a universal construction of a fuzzy ideal generated by a given fuzzy set in a ring. using this construction and employing the technique of strong level subsets, we provide the shortest and direct fuzzy set ...

We present several results related to van Douwen’s Problem, which asks whether there is homogeneous compactum with cellularity exceeding c, the cardinality of the reals. For example, just as all known homogeneous compacta have cellularity at most c, they satisfy similar upper bounds in terms of Peregudov’s Noetherian type and related cardinal functions defined by order-theoretic base properties...

We define a potentialist system of ZF-structures, that is, collection possible worlds in the language ZF connected by binary accessibility relation, achieving account full background set-theoretic universe $V$. The definition involves Berkeley cardinals, strongest known large cardinal axioms, inconsistent with Axiom Choice. In fact, as theory we assume just ZF. It turns out propositional modal ...