@article{1448610,
      recid = {1448610},
      author = {Tourlakis, George J.},
      title = {Computability /},
      publisher = {Springer,},
      address = {Cham :},
      pages = {1 online resource (652 pages)},
      year = {2022},
      abstract = {This survey of computability theory offers the techniques  and tools that computer scientists (as well as  mathematicians and philosophers studying the mathematical  foundations of computing) need to mathematically analyze  computational processes and investigate the theoretical  limitations of computing. Beginning with an introduction to  the mathematisation of "mechanical process" using URM  programs, this textbook explains basic theory such as  primitive recursive functions and predicates and  sequence-coding, partial recursive functions and  predicates, and loop programs. Features: Extensive and  mathematically complete coverage of the limitations of  logic, including Godels incompleteness theorems (first and  second), Rossers version of the first incompleteness  theorem, and Tarskis non expressibility of "truth"  Inability of computability to detect formal theorems  effectively, using Churchs proof of the unsolvability of  Hilberts Entscheidungsproblem Arithmetisation-free proof of  the pillars of computability: Kleenes s-m-n, universal  function and normal form theorems using "Churchs thesis"  and a simulation of the URM "register machine" by a  simultaneous recursion. These three pivotal results lead to  the deeper results of the theory Extensive coverage of the  advanced topic of computation with "oracles" including an  exposition of the search computability theory of  Moschovakis, the first recursion theorem, Turing  reducibility and Turing degrees and an application of the  Sacks priority method of "preserving agreements", and the  arithmetical hierarchy including Posts theorem Cobhams  mathematical characterisation of the concept deterministic  polynomial time computable function is fully proved A  complete proof of Blums speed-up theorem},
      url = {http://library.usi.edu/record/1448610},
      doi = {https://doi.org/10.1007/978-3-030-83202-5},
}