Currently displaying 1 – 7 of 7

Showing per page

Order by Relevance | Title | Year of publication

I teoremi di assolutezza in teoria degli insiemi: prima parte

Alessandro Andretta — 2003

Bollettino dell'Unione Matematica Italiana

Questa è la prima parte di una articolo espositivo dedicato ai teoremi di assolutezza, un argomento che sta assumendo un’importanza via via più grande in teoria degli insiemi. In questa prima parte vedremo come le questioni di teoria dei numeri non siano influenzate da assunzioni insiemistiche quali l’assioma di scelta o l’ipotesi del continuo.

Ordinary differential equations and descriptive set theory: uniqueness and globality of solutions of Cauchy problems in one dimension

Alessandro Andretta;  Alberto Marcone — 1997

Fundamenta Mathematicae

We study some natural sets arising in the theory of ordinary differential equations in one variable from the point of view of descriptive set theory and in particular classify them within the Borel hierarchy. We prove that the set of Cauchy problems for ordinary differential equations which have a unique solution is ∏ 2 0 -complete and that the set of Cauchy problems which locally have a unique solution is ∑ 3 0 -complete. We prove that the set of Cauchy problems which have a global solution is ∑ 0 4 -complete...

Pointwise convergence and the Wadge hierarchy

Alessandro Andretta;  Alberto Marcone — 2001

Commentationes Mathematicae Universitatis Carolinae

We show that if X is a Σ 1 1 separable metrizable space which is not σ -compact then C p * ( X ) , the space of bounded real-valued continuous functions on X with the topology of pointwise convergence, is Borel- Π 1 1 -complete. Assuming projective determinacy we show that if X is projective not σ -compact and n is least such that X is Σ n 1 then C p ( X ) , the space of real-valued continuous functions on X with the topology of pointwise convergence, is Borel- Π n 1 -complete. We also prove a simultaneous improvement of theorems of Christensen...

Borel-Wadge degrees

Alessandro Andretta;  Donald A. Martin — 2003

Fundamenta Mathematicae

Two sets of reals are Borel equivalent if one is the Borel pre-image of the other, and a Borel-Wadge degree is a collection of pairwise Borel equivalent subsets of ℝ. In this note we investigate the structure of Borel-Wadge degrees under the assumption of the Axiom of Determinacy.

Page 1

Download Results (CSV)