Hierarchy of Turing Degrees (eBook)

A Transfinite Hierarchy of Lowness Notions in the Computably Enumerable Degrees, Unifying Classes, and Natural Definability

Rod Downey, Noam Greenberg (Autoren)

eBook Download: PDF

2020
240 Seiten
Princeton University Press (Verlag)
978-0-691-20021-7 (ISBN)

Infos

Computability theory is a branch of mathematical logic and computer science that has become increasingly relevant in recent years. The field has developed growing connections in diverse areas of mathematics, with applications in topology, group theory, and other subfields.In A Hierarchy of Turing Degrees, Rod Downey and Noam Greenberg introduce a new hierarchy that allows them to classify the combinatorics of constructions from many areas of computability theory, including algorithmic randomness, Turing degrees, effectively closed sets, and effective structure theory. This unifying hierarchy gives rise to new natural definability results for Turing degree classes, demonstrating how dynamic constructions become reflected in definability. Downey and Greenberg present numerous construction techniques involving high-level nonuniform arguments, and their self-contained work is appropriate for graduate students and researchers.Blending traditional and modern research results in computability theory, A Hierarchy of Turing Degrees establishes novel directions in the field.

Produkt-Details

• Erscheint lt. Verlag: 16.6.2020
• Reihe/Serie: Annals of Mathematics Studies
• Reihe/Serie: Annals of Mathematics Studies
• Zusatzinfo: 3 b/w illus.
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik ► Theorie / Studium
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
• Schlagworte: algorithm • Algorithmic Learning Theory • AND gate • Antichain • Approximation • Arbitrarily large • arithmetic • bijection • Binary number • Cantor space • c.e. degrees • c.e. reals • Characteristic function (probability theory) • Clopen set • combination • combinatorics • Complexity • Computability • Computability Theory • computable analysis • computable function • computable model theory • Computable number • Computation • conjecture • Contradiction • corollary • Countable set • counterexample • Decision problem • Discrete space • Distributive lattice • Dyadic rational • Elaboration • Embedding • Empty string • Entscheidungsproblem • Enumeration • Gödel's Incompleteness Theorems • group theory • Halting Problem • I0 • Identity function • Iteration • Join and meet • lattice embeddings • Limit ordinal • Limit superior and limit inferior • Many-one reduction • Mathematical Induction • Mathematics • Maximal element • Maximal set • mind changes in computability theory • Model of computation • model Theory • modern computability theory • Modular lattice • Monograph • m-topped degrees • N0 • Natural number • Notation • Open set • ORDER BY • ordinal analysis • Ordinal arithmetic • pairwise • Parameter • partially ordered set • Payment • pi-zero-one classes • prompt permissions • Propositional Calculus • Quantity • randomness • Recursion (computer science) • recursion theory • Recursively enumerable set • relative recursive randomness • Requirement • Restriction (mathematics) • result • reverse mathematics • scientific notation • Self-Assembly • set theory • Simple set • small number • Subroutine • Subset • Summation • Theorem • theory • transfinite hierarchy of Turing degrees • Tree (data structure) • truth table • turing degree • Turing Machine • Turing reduction • Uncountable set • Undecidable problem • Unit interval • vertex cover • Without loss of generality • Word problem for groups • Word problem (mathematics)
• ISBN-10: 0-691-20021-1 / 0691200211
• ISBN-13: 978-0-691-20021-7 / 9780691200217