Constructibility and shiftings of view
Constructions of classes by transfinite induction in AST
Cuts of real classes
Definability degrees for classes in the alternative set theory
End-extending models of
Finite Embeddability of Sets and Ultrafilters
A set A of natural numbers is finitely embeddable in another such set B if every finite subset of A has a rightward translate that is a subset of B. This notion of finite embeddability arose in combinatorial number theory, but in this paper we study it in its own right. We also study a related notion of finite embeddability of ultrafilters on the natural numbers. Among other results, we obtain connections between finite embeddability and the algebraic and topological structure of the Stone-Čech...
Formes combinatoires du théorème d'incomplétude
Herbrand consistency and bounded arithmetic
We prove that the Gödel incompleteness theorem holds for a weak arithmetic Tₘ = IΔ₀ + Ωₘ, for m ≥ 2, in the form Tₘ ⊬ HCons(Tₘ), where HCons(Tₘ) is an arithmetic formula expressing the consistency of Tₘ with respect to the Herbrand notion of provability. Moreover, we prove , where is HCons relativised to the definable cut Iₘ of (m-2)-times iterated logarithms. The proof is model-theoretic. We also prove a certain non-conservation result for Tₘ.
Indicators, recursive saturation and expandability
Indiscernibles in the alternative set theory
Initial segments and isomorphic images of nonstandard models of arithmetic
La mathématique non standard vieille de soixante ans ?
Models of arithmetic and the 1-3-1 lattice
Monomorphisms of inductive number systems
More on extending automorphisms of models of Peano Arithmetic
Continuing the earlier research [Fund. Math. 129 (1988) and 149 (1996)] we give some information about extending automorphisms of models of PA to cofinal extensions.
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.
Non standard interpretations of higher order theories
Non-axiomatizable classes of V-topological fields.
Nonstandard arithmetic of function fields over H-convex subfields of *Q.
Nonstandard models of arithmetic as an alternative basis for continuum considerations