Computability theory | Wikipedia audio article

This is an audio version of the Wikipedia Article: https://en.wikipedia.org/wiki/Computability_theory 00:00:58 1 Computable and uncomputable sets 00:04:12 2 Turing computability 00:06:54 3 Areas of research 00:07:23 3.1 Relative computability and the Turing degrees 00:12:59 3.2 Other reducibilities 00:15:34 3.3 Rice's theorem and the arithmetical hierarchy 00:15:52 3.4 Reverse mathematics 00:16:55 3.5 Numberings 00:17:04 3.6 The priority method 00:17:46 3.7 The lattice of recursively enumerable sets 00:17:55 3.8 Automorphism problems 00:18:43 3.9 Kolmogorov complexity 00:20:29 3.10 Frequency computation 00:21:51 3.11 Inductive inference 00:23:34 3.12 Generalizations of Turing computability 00:24:48 3.13 Continuous computability theory 00:25:03 4 Relationships between definability, proof and computability 00:25:33 5 Name 00:25:43 6 Professional organizations 00:26:43 7 See also 00:28:04 8 Notes 00:28:38 9 References 00:30:44 10 External links 00:32:41 Professional organizations 00:33:09 See also Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago. Learning by listening is a great way to: - increases imagination and understanding - improves your listening skills - improves your own spoken accent - learn while on the move - reduce eye strain Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone. Listen on Google Assistant through Extra Audio: https://assistant.google.com/services/invoke/uid/0000001a130b3f91 Other Wikipedia audio articles at: https://www.youtube.com/results?search_query=wikipedia+tts Upload your own Wikipedia articles through: https://github.com/nodef/wikipedia-tts "There is only one good, knowledge, and one evil, ignorance." - Socrates SUMMARY ======= Computability theory, also known as recursion theory, is a branch of mathematical logic, of computer science, and of the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has since expanded to include the study of generalized computability and definability. In these areas, recursion theory overlaps with proof theory and effective descriptive set theory. Basic questions addressed by recursion theory include: What does it mean for a function on the natural numbers to be computable? How can noncomputable functions be classified into a hierarchy based on their level of noncomputability?Although there is considerable overlap in terms of knowledge and methods, mathematical recursion theorists study the theory of relative computability, reducibility notions, and degree structures; those in the computer science field focus on the theory of subrecursive hierarchies, formal methods, and formal languages.