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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].

Wajsberg algebras.

Josep M. Font, Antonio J. Rodríguez, Antoni Torrens (1984)

Stochastica

We present the basic theory of the most natural algebraic counterpart of the ℵ0-valued Lukasiewicz calculus, strictly logically formulated. After showing its lattice structure and its relation to C. C. Chang's MV-algebras we study the implicative filters and prove its equivalence to congruence relations. We present some properties of the variety of all Wajsberg algebras, among which there is a representation theorem. Finally we give some characterizations of linear, simple and semisimple algebras....

Weak Completeness Theorem for Propositional Linear Time Temporal Logic

Mariusz Giero (2012)

Formalized Mathematics

We prove weak (finite set of premises) completeness theorem for extended propositional linear time temporal logic with irreflexive version of until-operator. We base it on the proof of completeness for basic propositional linear time temporal logic given in [20] which roughly follows the idea of the Henkin-Hasenjaeger method for classical logic. We show that a temporal model exists for every formula which negation is not derivable (Satisfiability Theorem). The contrapositive of that theorem leads...

Weak Convergence and Weak Convergence

Keiko Narita, Yasunari Shidama, Noboru Endou (2015)

Formalized Mathematics

In this article, we deal with weak convergence on sequences in real normed spaces, and weak* convergence on sequences in dual spaces of real normed spaces. In the first section, we proved some topological properties of dual spaces of real normed spaces. We used these theorems for proofs of Section 3. In Section 2, we defined weak convergence and weak* convergence, and proved some properties. By RNS_Real Mizar functor, real normed spaces as real number spaces already defined in the article [18],...

Weak generic types and coverings of groups I

Ludomir Newelski, Marcin Petrykowski (2006)

Fundamenta Mathematicae

We introduce the notion of a weak generic type in a group. We improve our earlier results on countable coverings of groups and types.

Weak products of universal algebras

Ildikó Sain (1993)

Banach Center Publications

Weak direct products of arbitrary universal algebras are introduced. The usual notion for groups and rings is a special case. Some universal algebraic properties are proved and applications to cylindric and polyadic algebras are considered.

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 maximal decidable structures

Alexis Bès, Patrick Cégielski (2008)

RAIRO - Theoretical Informatics and Applications

We prove that there exists a structure M whose monadic second order theory is decidable, and such that the first-order theory of every expansion of M by a constant is undecidable. 


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.

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