Ordinal Definability And Recursion Theory Volume 3
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Author | : Alexander S. Kechris |
Publisher | : Cambridge University Press |
Total Pages | : 552 |
Release | : 2016-01-11 |
Genre | : Mathematics |
ISBN | : 1316586286 |
The proceedings of the Los Angeles Caltech-UCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Ordinal Definability and Recursion Theory is the third in a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes. Focusing on the subjects of 'HOD and its Local Versions' (Part V) and 'Recursion Theory' (Part VI), each of the two sections is preceded by an introductory survey putting the papers into present context. These four volumes will be a necessary part of the book collection of every set theorist.
Author | : Samuel Coskey |
Publisher | : American Mathematical Soc. |
Total Pages | : 207 |
Release | : 2020-06-18 |
Genre | : Education |
ISBN | : 1470443325 |
This volume contains the proceedings of Simon Fest, held in honor of Simon Thomas's 60th birthday, from September 15–17, 2017, at Rutgers University, Piscataway, New Jersey. The topics covered showcase recent advances from a variety of main areas of set theory, including descriptive set theory, forcing, and inner model theory, in addition to several applications of set theory, including ergodic theory, combinatorics, and model theory.
Author | : Andrés Eduardo Caicedo |
Publisher | : American Mathematical Soc. |
Total Pages | : 346 |
Release | : 2017-05-12 |
Genre | : Mathematics |
ISBN | : 1470422565 |
This volume contains the proceedings of the Logic at Harvard conference in honor of W. Hugh Woodin's 60th birthday, held March 27–29, 2015, at Harvard University. It presents a collection of papers related to the work of Woodin, who has been one of the leading figures in set theory since the early 1980s. The topics cover many of the areas central to Woodin's work, including large cardinals, determinacy, descriptive set theory and the continuum problem, as well as connections between set theory and Banach spaces, recursion theory, and philosophy, each reflecting a period of Woodin's career. Other topics covered are forcing axioms, inner model theory, the partition calculus, and the theory of ultrafilters. This volume should make a suitable introduction to Woodin's work and the concerns which motivate it. The papers should be of interest to graduate students and researchers in both mathematics and philosophy of mathematics, particularly in set theory, foundations and related areas.
Author | : Alexander S. Kechris |
Publisher | : Cambridge University Press |
Total Pages | : 317 |
Release | : 2020-11-05 |
Genre | : Mathematics |
ISBN | : 1107182999 |
The final volume in a series of four books presenting the seminal papers from the Caltech-UCLA 'Cabal Seminar'.
Author | : Paul B. Larson |
Publisher | : American Mathematical Society |
Total Pages | : 182 |
Release | : 2023-10-19 |
Genre | : Mathematics |
ISBN | : 1470472104 |
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 the Moschovakis Coding Lemma, the existence of strong partition cardinals, and the analysis of pointclasses in models of determinacy. The second half of the book introduces Woodin's axiom system $mathrm{AD}^{+}$ and presents his initial analysis of these axioms. These results include the consistency of $mathrm{AD}^{+}$ from the consistency of AD, and its local character and initial motivation. Proofs are given of fundamental results by Woodin, Martin, and Becker on the relationships among AD, $mathrm{AD}^{+}$, the Axiom of Real Determinacy, and the Suslin property. Many of these results are proved in print here for the first time. The book briefly discusses later work and fundamental questions which remain open. The study of models of $mathrm{AD}^{+}$ is an active area of contemporary research in set theory. The presentation is aimed at readers with a background in basic set theory, including forcing and ultrapowers. Some familiarity with classical results on regularity properties for sets of reals under AD is also expected.
Author | : Sophia Arbeiter |
Publisher | : Springer Nature |
Total Pages | : 526 |
Release | : |
Genre | : |
ISBN | : 3031584252 |
Author | : Katrin Tent |
Publisher | : Cambridge University Press |
Total Pages | : 259 |
Release | : 2012-03-08 |
Genre | : Mathematics |
ISBN | : 052176324X |
Concise introduction to current topics in model theory, including simple and stable theories.
Author | : Cyrus F. Nourani |
Publisher | : CRC Press |
Total Pages | : 304 |
Release | : 2016-02-24 |
Genre | : Mathematics |
ISBN | : 1771882484 |
This book, Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity, presents new techniques with functorial models to address important areas on pure mathematics and computability theory from the algebraic viewpoint. The reader is first introduced to categories and functorial models, with Kleene algebra examples
Author | : Merlin Carl |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 442 |
Release | : 2019-09-23 |
Genre | : Mathematics |
ISBN | : 3110492911 |
The series is devoted to the publication of high-level monographs on all areas of mathematical logic and its applications. It is addressed to advanced students and research mathematicians, and may also serve as a guide for lectures and for seminars at the graduate level.
Author | : Juliette Kennedy |
Publisher | : Cambridge University Press |
Total Pages | : 293 |
Release | : 2014-08-21 |
Genre | : Science |
ISBN | : 1139991752 |
The logician Kurt Gödel (1906–1978) published a paper in 1931 formulating what have come to be known as his 'incompleteness theorems', which prove, among other things, that within any formal system with resources sufficient to code arithmetic, questions exist which are neither provable nor disprovable on the basis of the axioms which define the system. These are among the most celebrated results in logic today. In this volume, leading philosophers and mathematicians assess important aspects of Gödel's work on the foundations and philosophy of mathematics. Their essays explore almost every aspect of Godel's intellectual legacy including his concepts of intuition and analyticity, the Completeness Theorem, the set-theoretic multiverse, and the state of mathematical logic today. This groundbreaking volume will be invaluable to students, historians, logicians and philosophers of mathematics who wish to understand the current thinking on these issues.