Die Nichtaxiomatisierbarkeit der unendlichwertigen Mengenlehre.
Dimension of indiscernibility equivalences
Dimensional compactness in biequivalence vector spaces
The notion of dimensionally compact class in a biequivalence vector space is introduced. Similarly as the notion of compactness with respect to a -equivalence reflects our nonability to grasp any infinite set under sharp distinction of its elements, the notion of dimensional compactness is related to the fact that we are not able to measure out any infinite set of independent parameters. A fairly natural Galois connection between equivalences on an infinite set and classes of set functions ...
Effective taxonomies and crossed taxonomies
Eine Erweiterung der NGB-Mengenlehre als Grundlage der Kategorientheorie
Endomorphic cuts and tails
Endomorphic universes and their standard extensions
Forcing in the alternative set theory. I
The technique of forcing is developed for the alternative set theory (AST) and similar weak theories, where it can be used to prove some new independence results. There are also introduced some new extensions of AST.
Forcing in the alternative set theory. II
By the technique of forcing, some new independence results are proved for the alternative set theory (AST) and similar weak theories: The scheme of choice is independent both of AST and of second order arithmetic, axiom of constructibility is independent of AST plus schemes of choice.
Fuzzy mappings and fuzzy sets
Fuzzy topologies
Homology theory in the alternative set theory I. Algebraic preliminaries
The notion of free group is defined, a relatively wide collection of groups which enable infinite set summation (called commutative -group), is introduced. Commutative -groups are studied from the set-theoretical point of view and from the point of view of free groups. Commutativity of the operator which is a special kind of inverse limit and factorization, is proved. Tensor product is defined, commutativity of direct product (also a free group construction and tensor product) with the special...
Homology theory in the AST II. Basic concepts, Eilenberg-Steenrod's axioms
Homology functor in the spirit of the AST is defined, its basic properties are studied. Eilenberg-Steenrod axioms for this functor are formulated and established.
How to handle fuzzy-quantities?
Indiscernibles in the alternative set theory
Inequivalence of the fragments of new foundations.
Internal and forcing models for the impredicative theory of classes [Book]
Laminations, or How to Build a Quantum-Logic-Valued Model of Set Theory.
Metamathematics of the alternative set theory. I.
Metamathematics of the alternative set theory. II.