Von Neumann regular rings and the Whitehead property of modules
Weak foundation and axioms of universality.
Weak variants of Martin's Axiom
Examples exist of smooth maps on the boundary of a smooth manifold M which allow continuous extensions over M without fixed points but no such smooth extensions. Such maps are studied here in more detail. They have a minimal fixed point set when all transversally fixed maps in their homotopy class are considered. Therefore we introduce a Nielsen fixed point theory for transversally fixed maps on smooth manifolds without or with boundary, and use it to calculate the minimum number of fixed points...
When a first order T has limit models
We sort out to a large extent when a (first order complete theory) T has a superlimit model in a cardinal λ. Also we deal with related notions of being limit.
When is the union of an increasing family of null sets?
We study the problem in the title and show that it is equivalent to the fact that every set of reals is an increasing union of measurable sets. We also show the relationship of it with Sierpi'nski sets.
Whitehead property of modules
Αll -dense sets of reals can be isomorphic
α-Properness and Axiom A
We show that under ZFC, for every indecomposable ordinal α < ω₁, there exists a poset which is β-proper for every β < α but not α-proper. It is also shown that a poset is forcing equivalent to a poset satisfying Axiom A if and only if it is α-proper for every α < ω₁.
Δ₁-Definability of the non-stationary ideal at successor cardinals
Assuming V = L, for every successor cardinal κ we construct a GCH and cardinal preserving forcing poset ℙ ∈ L such that in the ideal of all non-stationary subsets of κ is Δ₁-definable over H(κ⁺).
-directedness and a question of E. Michael
We define -directedness, investigate various properties to determine whether they have this property or not, and use our results to obtain easier proofs of theorems due to Laurence and Alster concerning the existence of a Michael space, i.eȧ Lindelöf space whose product with the irrationals is not Lindelöf.
ωι-Sonslin trees under countable support iterations
We show the property “is proper and preserves every -Souslin tree” is preserved by countable support iteration.
О генетических моделях.
О границах применимости принципа рефлексии.
О противоречивости метатеории Нудельмана
Общая теория бесконечно малых.