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A Hierarchy of Turing Degrees
Noam Greenberg, Rod Downey
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
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.
Kundenbewertungen
Tree (data structure), Arithmetic, Discrete space, Word problem (mathematics), Maximal element, Modular lattice, Entscheidungsproblem, Enumeration, Elaboration, Decision problem, Limit ordinal, Gödel's incompleteness theorems, Order by, Computable analysis, Identity function, Subset, Dyadic rational, Counterexample, Reverse mathematics, Unit interval, Word problem for groups, Embedding, Turing machine, Model of computation, Computable function, Set theory, Theorem, Maximal set, Algorithmic learning theory, Ordinal arithmetic, Approximation, Algorithm, Open set, Recursively enumerable set, Summation, Combination, Computability theory, Arbitrarily large, Mathematics, Mathematical induction, Characteristic function (probability theory), I0, Computability, Binary number, Vertex cover, Combinatorics, Notation, Restriction (mathematics), Turing reduction, Iteration, Natural number, Requirement, Propositional calculus, Computation, Distributive lattice, Quantity, Partially ordered set, Pairwise, AND gate, Result, Scientific notation, Join and meet, N0, Turing degree, Truth table, Halting problem, Computable number, Limit superior and limit inferior, Recursion (computer science), Ordinal analysis