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An Isomorphic Classification of C ( 2 × [ 0 , α ] ) Spaces

Elói Medina Galego (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

We present an extension of the classical isomorphic classification of the Banach spaces C([0,α]) of all real continuous functions defined on the nondenumerable intervals of ordinals [0,α]. As an application, we establish the isomorphic classification of the Banach spaces C ( 2 × [ 0 , α ] ) of all real continuous functions defined on the compact spaces 2 × [ 0 , α ] , the topological product of the Cantor cubes 2 with smaller than the first sequential cardinal, and intervals of ordinal numbers [0,α]. Consequently, it is relatively...

An o-minimal structure which does not admit C ∞ cellular decomposition

Olivier Le Gal, Jean-Philippe Rolin (2009)

Annales de l’institut Fourier

We present an example of an o-minimal structure which does not admit C ∞ cellular decomposition. To this end, we construct a function H whose germ at the origin admits a C k representative for each integer k , but no C ∞ representative. A number theoretic condition on the coefficients of the Taylor series of H then insures the quasianalyticity of some differential algebras 𝒜 n ( H ) induced by H . The o-minimality of the structure generated by H is deduced from this quasianalyticity property.

An ordered structure of pseudo-BCI-algebras

Ivan Chajda, Helmut Länger (2016)

Mathematica Bohemica

In Chajda's paper (2014), to an arbitrary BCI-algebra the author assigned an ordered structure with one binary operation which possesses certain antitone mappings. In the present paper, we show that a similar construction can be done also for pseudo-BCI-algebras, but the resulting structure should have two binary operations and a set of couples of antitone mappings which are in a certain sense mutually inverse. The motivation for this approach is the well-known fact that every commutative BCK-algebra...

An ordered structure of rank two related to Dulac's Problem

A. Dolich, P. Speissegger (2008)

Fundamenta Mathematicae

For a vector field ξ on ℝ² we construct, under certain assumptions on ξ, an ordered model-theoretic structure associated to the flow of ξ. We do this in such a way that the set of all limit cycles of ξ is represented by a definable set. This allows us to give two restatements of Dulac’s Problem for ξ - that is, the question whether ξ has finitely many limit cycles-in model-theoretic terms, one involving the recently developed notion of U þ -rank and the other involving the notion of o-minimality.

An upper bound on the space complexity of random formulae in resolution

Michele Zito (2002)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We prove that, with high probability, the space complexity of refuting a random unsatisfiable Boolean formula in k -CNF on n variables and m = Δ n clauses is O n · Δ - 1 k - 2 .

Analyse relative

Yves Peraire (1992)

Annales scientifiques de l'Université de Clermont. Mathématiques

Analytic determinacy and 0# A forcing-free proof of Harrington’s theorem

Ramez Sami (1999)

Fundamenta Mathematicae

We prove the following theorem: Given a⊆ω and 1 ≤ α < ω 1 C K , if for some η < ℵ 1 and all u ∈ WO of length η, a is Σ α 0 ( u ) , then a is Σ α 0 . We use this result to give a new, forcing-free, proof of Leo Harrington’s theorem: Σ 1 1 -Turing-determinacy implies the existence of 0 .

Analytic gaps

Stevo Todorčević (1996)

Fundamenta Mathematicae

We investigate when two orthogonal families of sets of integers can be separated if one of them is analytic.

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