A note on cofinal extensions and segments
-structures
Monotonic valuations and valuations of triads of higher types
End-extensions of countable structures and the induction schema
Compactness and homogeneity of saturated structures. I.
Approximations of -classes and -classes
Correction to the paper: “Set-like equivalence and inner and outer cuts”
Some automorphisms of natural numbers in the alternative set theory
Twin prime problem in an arithmetic without induction
Compactness and homogeneity of saturated structures. II.
Set-like equivalence and inner and outer cuts
Combinatoric properties of classes in AST
A representation of models of Peano arithmetic
Valuations of structures
Valuations of lines
We enlarge the problem of valuations of triads on so called lines. A line in an -structure (it means that is a semigroup and is an automorphism or an antiautomorphism on such that ) is, generally, a sequence , , (where is the class of finite integers) of substructures of such that holds for each . We denote this line as and we say that a mapping is a valuation of the line in a line if it is, for each , a valuation of the triad in . Some theorems on an existence of...
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...
-representation and set-prolongations
By an -representation of a relation we mean its isomorphic embedding to . Some theorems on such a representation are presented. Especially, we prove a version of the well-known theorem on isomorphic representation of extensional and well-founded relations in , which holds in Zermelo-Fraenkel set theory. This our version is in Zermelo-Fraenkel set theory false. A general theorem on a set-prolongation is proved; it enables us to solve the task of the representation in question.
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