Metamathematics of the alternative set theory. I.
Metamathematics of the alternative set theory. II.
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.