Results 261 to 270 of about 151,811 (297)
Some of the next articles are maybe not open access.
Analytic sets in Descriptive Set Theory and NP sets in Complexity Theory
Fundamenta Informaticae, 2002Motivated by the analogy ``(NP/Poly)∼analytic'', we propose a co-analytic set W whose finite equivalent W_finite is coNP-complete. The complement of W is in fact a variant of ``infinite clique''. A combinatorial proof of the non-analyticity of W is produced and studied in order to be (eventually) ``finitized'' into a probabilistic proof of ``W_finite ∉
openaire +3 more sources
1970
The notion of a ‘set’, or collection of objects, is basic, both in our daily lives and in mathematics. As we grow up, we become aware of collections of toys, groups of people, families of relatives, heaps of sand, classes of schoolchildren, mobs of rioters, and whole lists of collective nouns.
H. B. Griffiths, P. J. Hilton
openaire +1 more source
The notion of a ‘set’, or collection of objects, is basic, both in our daily lives and in mathematics. As we grow up, we become aware of collections of toys, groups of people, families of relatives, heaps of sand, classes of schoolchildren, mobs of rioters, and whole lists of collective nouns.
H. B. Griffiths, P. J. Hilton
openaire +1 more source
Louveau's theorem for the descriptive set theory of internal sets
Journal of Symbolic Logic, 1997AbstractWe give positive answers to two open questions from [15]. (1) For every set C countably determined over , if C is then it must be over , and (2) every Borel subset of the product of two internal sets X and Y all of whose vertical sections are can be represented as an intersection (union) of Borel sets with vertical sections of lower Borel ...
Kenneth Schilling, Bosko Zivaljevic
openaire +2 more sources
2011
In 1905 Henri Lebesgue [1905] published a large paper Sur les fonctions representables analytiquement, which strongly influenced the next investigations in a domain of mathematics that we call today the descriptive set theory. The paper was mainly devoted to the study of the Baire Hierarchy of real functions. Moreover, a proof of one theorem was wrong (
openaire +1 more source
In 1905 Henri Lebesgue [1905] published a large paper Sur les fonctions representables analytiquement, which strongly influenced the next investigations in a domain of mathematics that we call today the descriptive set theory. The paper was mainly devoted to the study of the Baire Hierarchy of real functions. Moreover, a proof of one theorem was wrong (
openaire +1 more source
1997
Descriptive set theory deals with sets of reals that are described in some simple way: sets that have a simple topological structure (e.g., continuous images of closed sets) or are definable in a simple way. The main theme is that questions that are difficult to answer if asked for arbitrary sets of reals, become much easier when asked for sets that ...
openaire +1 more source
Descriptive set theory deals with sets of reals that are described in some simple way: sets that have a simple topological structure (e.g., continuous images of closed sets) or are definable in a simple way. The main theme is that questions that are difficult to answer if asked for arbitrary sets of reals, become much easier when asked for sets that ...
openaire +1 more source
Descriptive Set Theory: Projective Sets
1977Publisher Summary This chapter describes classical and effective descriptive set theory, with emphasis mainly on projective sets. The chapter provides an account of the revival in this subject that has taken place in the past 10 years, a revival based on strong set theoretic hypotheses—notably, projective determinacy.
openaire +1 more source
Towards the Effective Descriptive Set Theory
2015We prove effective versions of some classical results about measurable functions and derive from this extensions of the Suslin-Kleene theorem, and of the effective Hausdorff theorem for the computable Polish spaces (this was established in [2] with a different proof) and for the computable \(\omega \)-continuous domains (this answers an open question ...
openaire +1 more source
“Hyperfinite” descriptive set theory
2004Descriptive set theory studies those subsets of topological spaces (called pointsets) which can be defined, by means of a list of specified operations including, e.g., complement, countable union and intersection, projection, beginning with open sets of the space.
Vladimir Kanovei, Michael Reeken
openaire +1 more source
Notes on Descriptive Set Theory
In the first chapter we present briefly the concepts, which are needed throughout the book.openaire +1 more source