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  "body": "\n## Summary\n\nComputability theory, also called recursion theory, studies which functions and sets of natural numbers can be computed by an algorithm.\nIts basic objects are [[computable functions|KZSB5E471K]], defined through [[Turing machines|758EYCN27B]] or through [[general recursive functions|HBK5QHC1GC]].\nIt proves that some problems, such as the [[halting problem|Z7TN2B35B0]], have no algorithmic solution.\nIt then compares unsolvable problems by reductions, which leads to [[Turing degrees|P5N2ND3VCG]] and to hierarchies of definable sets.\n\n## Explanations\n\n### L1 human\n\nAn algorithm is a finite list of exact instructions that a machine can follow.\nComputability theory asks which questions about numbers can be answered by such a list, with no limit on time or memory.\nChecking whether a number is prime is computable: try all smaller divisors.\nDeciding whether an arbitrary program stops on a given input is not computable, and this can be proved.\nThe theory also measures how far an unsolvable problem is from being solvable.\n",
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