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Wadge degrees of ω -languages of deterministic Turing machines

Victor Selivanov (2003)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We describe Wadge degrees of ω -languages recognizable by deterministic Turing machines. In particular, it is shown that the ordinal corresponding to these degrees is ξ ω where ξ = ω 1 CK is the first non-recursive ordinal known as the Church–Kleene ordinal. This answers a question raised in [2].

Wadge Degrees of ω-Languages of Deterministic Turing Machines

Victor Selivanov (2010)

RAIRO - Theoretical Informatics and Applications

We describe Wadge degrees of ω-languages recognizable by deterministic Turing machines. In particular, it is shown that the ordinal corresponding to these degrees is ξω where ξ = ω1CK is the first non-recursive ordinal known as the Church–Kleene ordinal. This answers a question raised in [2].

Weak Rudin-Keisler reductions on projective ideals

Konstantinos A. Beros (2016)

Fundamenta Mathematicae

We consider a slightly modified form of the standard Rudin-Keisler order on ideals and demonstrate the existence of complete (with respect to this order) ideals in various projective classes. Using our methods, we obtain a simple proof of Hjorth’s theorem on the existence of a complete Π¹₁ equivalence relation. This proof enables us (under PD) to generalize Hjorth’s result to the classes of Π ¹ 2 n + 1 equivalence relations.

Weak square sequences and special Aronszajn trees

John Krueger (2013)

Fundamenta Mathematicae

A classical theorem of set theory is the equivalence of the weak square principle μ * with the existence of a special Aronszajn tree on μ⁺. We introduce the notion of a weak square sequence on any regular uncountable cardinal, and prove that the equivalence between weak square sequences and special Aronszajn trees holds in general.

Weak variants of Martin's Axiom

J. Barnett (1992)

Fundamenta Mathematicae

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...

Weakly normal ideals ou PKl and the singular cardinal hypothesis

Yoshihiro Abe (1993)

Fundamenta Mathematicae

In §1, we observe that a weakly normal ideal has a saturation property; we also show that the existence of certain precipitous ideals is sufficient for the existence of weakly normal ideals. In §2, generalizing Solovay’s theorem concerning strongly compact cardinals, we show that λ < κ is decided if P κ λ carries a weakly normal ideal and λ is regular or cf λ ≤ κ. This is applied to solving the singular cardinal hypothesis.

Weighted sums of aggregation operators.

Tomasa Calvo, Bernard De Baets, Radko Mesiar (1999)

Mathware and Soft Computing

The aim of this work is to investigate when a weighted sum, or in other words, a linear combination, of two or more aggregation operators leads to a new aggregation operator. For weights belonging to the real unit interval, we obtain a convex combination and the answer is known to be always positive. However, we will show that also other weights can be used, depending upon the aggregation operators involved. A first set of suitable weights is obtained by a general method based on the variation of...

Well-quasi-ordering Aronszajn lines

Carlos Martinez-Ranero (2011)

Fundamenta Mathematicae

We show that, assuming PFA, the class of all Aronszajn lines is well-quasi-ordered by embeddability.

When a first order T has limit models

Saharon Shelah (2012)

Colloquium Mathematicae

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 does the Katětov order imply that one ideal extends the other?

Paweł Barbarski, Rafał Filipów, Nikodem Mrożek, Piotr Szuca (2013)

Colloquium Mathematicae

We consider the Katětov order between ideals of subsets of natural numbers (" K ") and its stronger variant-containing an isomorphic ideal ("⊑ "). In particular, we are interested in ideals for which K for every ideal . We find examples of ideals with this property and show how this property can be used to reformulate some problems known from the literature in terms of the Katětov order instead of the order "⊑ " (and vice versa).

When is 𝐍 Lindelöf?

Horst Herrlich, George E. Strecker (1997)

Commentationes Mathematicae Universitatis Carolinae

Theorem. In ZF (i.e., Zermelo-Fraenkel set theory without the axiom of choice) the following conditions are equivalent: (1) is a Lindelöf space, (2) is a Lindelöf space, (3) is a Lindelöf space, (4) every topological space with a countable base is a Lindelöf space, (5) every subspace of is separable, (6) in , a point x is in the closure of a set A iff there exists a sequence in A that converges to x , (7) a function f : is continuous at a point x iff f is sequentially continuous at x , (8)...

When is the union of an increasing family of null sets?

Juan González-Hernández, Fernando Hernández-Hernández, César E. Villarreal (2007)

Commentationes Mathematicae Universitatis Carolinae

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.

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