College Publications logo   College Publications title  
View Basket
Homepage Contact page
Academia Brasileira de Filosofia
Cadernos de Lógica e Computação
Cadernos de Lógica e Filosofia
Cahiers de Logique et d'Epistemologie
Communication, Mind and Language
Comptes Rendus de l'Academie Internationale de Philosophie des Sciences
Cuadernos de lógica, Epistemología y Lenguaje
Encyclopaedia of Logic
Historia Logicae
IfColog series in Computational Logic
Journal of Applied Logics - IfCoLog Journal
Logics for New-Generation AI
Logic and Law
Logic and Semiotics
Logic PhDs
Logic, Methodology and Philosophy of Science
The Logica Yearbook
Marked States
Neural Computing and Artificial Intelligence
The SILFS series
Studies in Logic
Studies in Talmudic Logic
Student Publications
Texts in Logic and Reasoning
Texts in Mathematics
Digital Downloads
Information for authors
About us
Search for Books



A Mathematical Primer on Computability

Amilcar Sernadas, Cristina Sernadas and Joao Rasga

he book provides a self-contained introduction to computability theory for advanced undergraduate or early graduate students of mathematics and computer science. The technical material is illustrated with plenty of examples, problems with fully worked solutions as well as a range of proposed exercises.

Part I is centered around fundamental computability notions and results, starting with the pillar concepts of computational model (an abstract high-level programming language), computable function, decidable and listable set, proper universal function, decision problem and the reduction technique for transferring decidability and listability properties. The essential results namely Rice’s Theorem, Rice-Shapiro’s Theorem, Rice-Shapiro-McNaughton-Myhill’s Theorem as well as Rogers’ Theorem and the Recursion Theorem are presented and illustrated. Many-to-one reducibility and many-to-one degrees are investigated. A short introduction to computation with oracles is also included. Computable as well as non-computable operators are introduced as well as monotonic and finitary operators. The relationship between them is discussed, in particular via Myhill-Shepherdson’s Theorem. Kleene’s Least Fixed Point Theorem is also presented. Finally, Part I terminates with a BRiefing on the Turing computational model, Turing reducibility and Turing degrees.
Part II of the book concentrates on applications of computability in several areas namely in logic (undecidability of arithmetic, satisfiability in propositional logic, decidability in modal logic), Euclidean geometry, graphs and Kolmogorov complexity. Nevertheless no previous knowledge of these subjects is required. The essential details for understanding the applications are provided.

7 November 2018


For Digital Download:
Buy now

© 2005–2024 College Publications / VFH webmaster