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AuthorSanchis, Luis E. author
TitleReflexive Structures [electronic resource] : An Introduction to Computability Theory / by Luis E. Sanchis
ImprintNew York, NY : Springer New York, 1988
Connect tohttp://dx.doi.org/10.1007/978-1-4612-3878-2
Descript XII, 233 p. online resource

SUMMARY

Reflexive Structures: An Introduction to Computability Theory is concerned with the foundations of the theory of recursive functions. The approach taken presents the fundamental structures in a fairly general setting, but avoiding the introduction of abstract axiomatic domains. Natural numbers and numerical functions are considered exclusively, which results in a concrete theory conceptually organized around Church's thesis. The book develops the important structures in recursive function theory: closure properties, reflexivity, enumeration, and hyperenumeration. Of particular interest is the treatment of recursion, which is considered from two different points of view: via the minimal fixed point theory of continuous transformations, and via the well known stack algorithm. Reflexive Structures is intended as an introduction to the general theory of computability. It can be used as a text or reference in senior undergraduate and first year graduate level classes in computer science or mathematics


CONTENT

1 Functions and Predicates -- ยง1. Definitions -- ยง2. Numerical Functions -- ยง3. Finitary Rules -- ยง4. Closure Properties -- ยง5. Minimal Closure -- ยง6. More Elementary Functions and Predicates -- 2 Recursive Functions -- ยง1. Primitive Recursion -- ยง2. Functional Transformations -- ยง3. Recursive Specifications -- ยง4. Recursive Evaluation -- ยง5. Churchโ{128}{153}s Thesis -- 3 Enumeration -- ยง1. Predicate Classes -- ยง2. Enumeration Properties -- ยง3. Induction -- ยง4. Nondeterministic Computability -- 4 Reflexive Structures -- ยง1. Interpreters -- ยง2. A Universal Interpreter -- ยง3. Two Constructions -- ยง4. The Recursion Theorem -- ยง5. Relational Structures -- ยง6. Uniform Structures -- 5 Hyperenumeration -- ยง1. Function Quantification -- ยง2. Nonfinitary Induction -- ยง3. Functional Induction -- ยง4. Ordinal Notations -- ยง5. Reflexive Systems -- ยง6. Hyperhyperenumeration -- References


Mathematics Computer science Computers Mathematical logic Mathematics Mathematical Logic and Foundations Computation by Abstract Devices Computer Science general



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