Subsystems of Second-order Arithmetic, and Descriptive Set Theory Under the Axiom of Determinateness
Title | Subsystems of Second-order Arithmetic, and Descriptive Set Theory Under the Axiom of Determinateness PDF eBook |
Author | Robert Alan Van Wesep |
Publisher | |
Pages | 242 |
Release | 1977 |
Genre | |
ISBN |
Subsystems of Second Order Arithmetic
Title | Subsystems of Second Order Arithmetic PDF eBook |
Author | Stephen George Simpson |
Publisher | Cambridge University Press |
Pages | 461 |
Release | 2009-05-29 |
Genre | Mathematics |
ISBN | 052188439X |
This volume examines appropriate axioms for mathematics to prove particular theorems in core areas.
Subsystems of Second Order Arithmetic
Title | Subsystems of Second Order Arithmetic PDF eBook |
Author | Stephen G. Simpson |
Publisher | |
Pages | 444 |
Release | 1999 |
Genre | Computer science |
ISBN | 9783642599712 |
"From the point of view of the foundations of mathematics, this definitive work by Simpson is the most anxiously awaited monograph for over a decade. The "subsystems of second order arithmetic" provide the basic formal systems normally used in our current understanding of the logical structure of classical mathematics. Simpson provides an encyclopedic treatment of these systems with an emphasis on *Hilbert's program* (where infinitary mathematics is to be secured or reinterpreted by finitary mathematics), and the emerging *reverse mathematics* (where axioms necessary for providing theorems are determined by deriving axioms from theorems). The classical mathematical topics treated in these axiomatic terms are very diverse, and include standard topics in complete separable metric spaces and Banach spaces, countable groups, rings, fields, and vector spaces, ordinary differential equations, fixed points, infinite games, Ramsey theory, and many others. The material, with its many open problems and detailed references to the literature, is particularly valuable for proof theorists and recursion theorists. The book is both suitable for the beginning graduate student in mathematical logic, and encyclopedic for the expert." Harvey Friedman, Ohio State University.
Revolutions and Revelations in Computability
Title | Revolutions and Revelations in Computability PDF eBook |
Author | Ulrich Berger |
Publisher | Springer Nature |
Pages | 374 |
Release | 2022-06-25 |
Genre | Computers |
ISBN | 3031087402 |
This book constitutes the proceedings of the 18th Conference on Computability in Europe, CiE 2022, in Swansea, UK, in July 2022. The 19 full papers together with 7 invited papers presented in this volume were carefully reviewed and selected from 41 submissions. The motto of CiE 2022 was “Revolutions and revelations in computability”. This alludes to the revolutionary developments we have seen in computability theory, starting with Turing's and Gödel's discoveries of the uncomputable and the unprovable and continuing to the present day with the advent of new computational paradigms such as quantum computing and bio-computing, which have dramatically changed our view of computability and revealed new insights into the multifarious nature of computation.
Descriptive Set Theory and Definable Forcing
Title | Descriptive Set Theory and Definable Forcing PDF eBook |
Author | Jindřich Zapletal |
Publisher | American Mathematical Soc. |
Pages | 158 |
Release | 2004 |
Genre | Mathematics |
ISBN | 0821834509 |
Focuses on the relationship between definable forcing and descriptive set theory; the forcing serves as a tool for proving independence of inequalities between cardinal invariants of the continuum.
Axiomatic Set Theory, Part 1
Title | Axiomatic Set Theory, Part 1 PDF eBook |
Author | Dana S. Scott |
Publisher | American Mathematical Soc. |
Pages | 482 |
Release | 1971-12-31 |
Genre | Mathematics |
ISBN | 0821802453 |
A Formalization of Set Theory Without Variables
Title | A Formalization of Set Theory Without Variables PDF eBook |
Author | Alfred Tarski |
Publisher | American Mathematical Soc. |
Pages | 344 |
Release | |
Genre | Mathematics |
ISBN | 9780821874745 |
Culminates nearly half a century of the late Alfred Tarski's foundational studies in logic, mathematics, and the philosophy of science. This work shows that set theory and number theory can be developed within the framework of a new, different and simple equational formalism, closely related to the formalism of the theory of relation algebras.