Metamathematics of the alternative set theory. III.
Minimal monads
Minimal ultrafilters and maximal endomorphic universes
Models of AST without choice
Model-theoretical constructions in AST. I.
Monads in basic equivalences
Monads of indiscernibles
Monotonic valuations and valuations of triads of higher types
Monotonic valuations of -triads and evaluations of ideals
We develop problems of monotonic valuations of triads. A theorem on monotonic valuations of triads of the type is presented. We study, using the notion of the monotonic valuation, representations of ideals by monotone and subadditive mappings. We prove, for example, that there exists, for each ideal of the type on a set , a monotone and subadditive set-mapping on with values in non-negative rational numbers such that . Some analogical results are proved for ideals of the types and...
Multiplication of nonadditive cuts in AST
Three complete characteristics of couples of nonadditive cuts such that are given. The equality is proved for all couples of nonadditive cuts. Some examples of nonadditive cuts are described.
Nonstandard models of arithmetic as an alternative basis for continuum considerations
Notes on revealed classes
On a weak Kelley-Morse theory of classes
On fuzzy-quantities with real and integer values
On models in the alternative set theory
On sentences provable in impredicative extensions of theories [Book]
On the adjunction of any semiset to the system of -classes in AST
On the algebraic structure of fuzzy sets of type 2
On the existence of factor sets by external equivalences in IST.
On the number of models of the Kelley-Morse theory of classes