Notes on revealed classes
O struktuře modelů omezené -indukce
On elementary cuts in recursively saturated models of Peano Arithmetic
On External Properties of Nonstandard Models of Arithmetic
On regular interstices and selective types in countable arithmetically saturated models of Peano Arithmetic
We continue the earlier research of [1]. In particular, we work out a class of regular interstices and show that selective types are realized in regular interstices. We also show that, contrary to the situation above definable elements, the stabilizer of an element inside M(0) whose type is selective need not be maximal.
On Sigma10-extensions of Omega
On some problems in
On the adjunction of any semiset to the system of -classes in AST
On the strength of several versions of Dirichlet's ("Pigeon-Hole"-) principle in the sense of first-order logic.
On -extensions of .
Ordered ultraconnected rings
Order-types of models of arithmetic and a connection with arithmetic saturation.
Revealed automorphisms
We study automorphisms in the alternative set theory. We prove that fully revealed automorphisms are not closed under composition. We also construct some special automorphisms. We generalize the notion of revealment and Sd-class.
Some automorphisms of natural numbers in the alternative set theory
Some remarks to the axiom of prolongation
Strong initial segments of models of IΔ₀
McAloon showed that if 𝓐 is a nonstandard model of IΔ₀, then some initial segment of 𝓐 is a nonstandard model of PA. Sommer and D'Aquino characterized, in terms of the Wainer functions, the elements that can belong to such an initial segment. The characterization used work of Ketonen and Solovay, and Paris. Here we give conditions on a model 𝓐 of IΔ₀ guaranteeing that there is an n-elementary initial segment that is a nonstandard model of PA. We also characterize the elements that can be included....
Unions and Intersections of Isomoryhic Images of Nonstandard Models of Arithmetic
ω-models of second order arithmetic and admissible sets
Нестандартный анализ и аксиома детерминированности