This is an expository account of work on strong forms of the Axiom of Determinacy (AD) by a group of set theorists in Southern California, in particular by W. Hugh Woodin. The first half of the book reviews necessary background material, including...Loe edasi...
We provide analogues of the results from Friedman and Motto Ros (2011) and Camerlo, Marcone, and Motto Ros (2013) (which correspond to the case) for arbitrary -Souslin quasi-orders on any Polish space, for an infinite cardinal smaller than the cardi...Loe edasi...
We solve a number of questions pertaining to the dynamics of linear operators on Hilbert spaces, sometimes by using Baire category arguments and sometimes by constructing explicit examples. In particular, we prove the following results. (i) A typica...Loe edasi...
Friedman and Schrittesser set out to answer a long-standing question regarding Lebesgue measurability and the Baire property, and how their behavior can differ with respect to sets in the projective hierarchy. Namely, they prove the theorem if ZF...Loe edasi...
Larson and Zapletal introduce geometric set theory as a new area of mathematics that compares transitive models of set theory with respect to the extensional agreement and definability. Looking first at equivalence relations, they consider the vi...Loe edasi...
Presents Results from a Very Active Area of ResearchExploring an active area of mathematics that studies the complexity of equivalence relations and classification problems, Invariant Descriptive...Loe edasi...
Woodin has been a leading figure in set theory since the early 1980s, and colleagues, former students, and other mathematicians wish him happy birthday with 12 papers on matters of interest to him. Their topics include the enumeration of degrees:...Loe edasi...
Sari: Theoretical Computer Science and General Issues
(Ilmumisaeg: 06-Aug-2016, Paperback / softback, Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, ISBN-13: 9783662529461)
The book is based on the PhD thesis Descriptive Set Theoretic Methods in Automata Theory, awarded the E.W. Beth Prize in 2015 for outstanding dissertations in the fields of logic, language, and information. The thesis reveals unexpected connections...Loe edasi...
Descriptive Set Theory is the study of sets in separable, complete metric spaces that can be defined (or constructed), and so can be expected to have special properties not enjoyed by arbitrary pointsets. This subject was started by the French analy...Loe edasi...
(Ilmumisaeg: 30-Jul-2009, Hardback, Kirjastus: American Mathematical Society, ISBN-13: 9780821848135)
The first edition was published in 1980 as volume 100 in the Studies in Logic series of North Holland, and Moschovakis says only parts have been substantially rewritten to incorporate new findings, but known errors have been corrected and the bibliog...Loe edasi...
Gao (mathematics, U. of North Texas) presents a study of equivalence relations and classification problems that includes an introduction to basic concepts as well as a review of classical descriptions of set theory. With exercises and examples he exp...Loe edasi...
(Ilmumisaeg: 07-Feb-2008, Hardback, Kirjastus: Cambridge University Press, ISBN-13: 9780521874267)
Unites descriptive set theory and definable proper forcing and explores the relations between them. Both forcing and descriptive set theory are explained independently, their sub-areas described, following their commitment to each other. This text hi...Loe edasi...
The authors present some surprising connections that sets of uniqueness for trigonometic series have with descriptive set theory. They present many new results concerning the structure of sets of uniqueness and include solutions to some of the classi...Loe edasi...
