O struktuře modelů omezené -indukce
On elementary cuts in recursively saturated models of Peano Arithmetic
On embedding models of arithmetic of cardinality ℵ₁ into reduced powers
In the early 1970’s S. Tennenbaum proved that all countable models of PA₁¯ + ∀₁ -Th(ℕ) are embeddable into the reduced product , where ℱ is the cofinite filter. In this paper we show that if M is a model of PA¯ + ∀₁ - Th(ℕ), and |M| = ℵ₁, then M is embeddable into , where D is any regular filter on ω.
On expandability of models of arithmetic and set theory to models of weak second-order theories
On extending automorphisms of models of Peano Arithmetic
Continuing the earlier research in [10] we give some information on extending automorphisms of models of PA to end extensions and cofinal extensions.
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 the Leibniz-Mycielski axiom in set theory
Motivated by Leibniz’s thesis on the identity of indiscernibles, Mycielski introduced a set-theoretic axiom, here dubbed the Leibniz-Mycielski axiom LM, which asserts that for each pair of distinct sets x and y there exists an ordinal α exceeding the ranks of x and y, and a formula φ(v), such that satisfies φ(x) ∧¬ φ(y). We examine the relationship between LM and some other axioms of set theory. Our principal results are as follows: 1. In the presence of ZF, the following are equivalent: (a) LM. (b)...
Order-types of models of arithmetic and a connection with arithmetic saturation.