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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.

Analytic partial orders and oriented graphs

Alain Louveau (2006)

Fundamenta Mathematicae

We prove that there is no maximum element, under Borel reducibility, in the class of analytic partial orders and in the class of analytic oriented graphs. We also provide a natural jump operator for these two classes.

Currently displaying 601 – 620 of 724