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completely recursively

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  • automata theory — Body of physical and logical principles underlying the operation of any electromechanical device (an automaton) that converts information input in one form into another, or into some action, according to an algorithm. Norbert Wiener and Alan M.… …   Universalium

  • Recursion theory — Recursion theory, also called computability theory, is a branch of mathematical logic that originated in the 1930s with the study of computable functions and Turing degrees. The field has grown to include the study of generalized computability… …   Wikipedia

  • Computability theory — For the concept of computability, see Computability. Computability theory, also called recursion theory, is a branch of mathematical logic that originated in the 1930s with the study of computable functions and Turing degrees. The field has grown …   Wikipedia

  • Halting problem — In computability theory, the halting problem can be stated as follows: Given a description of a computer program, decide whether the program finishes running or continues to run forever. This is equivalent to the problem of deciding, given a… …   Wikipedia

  • mathematics, foundations of — Scientific inquiry into the nature of mathematical theories and the scope of mathematical methods. It began with Euclid s Elements as an inquiry into the logical and philosophical basis of mathematics in essence, whether the axioms of any system… …   Universalium

  • Lambda calculus — In mathematical logic and computer science, lambda calculus, also written as λ calculus, is a formal system designed to investigate function definition, function application and recursion. It was introduced by Alonzo Church and Stephen Cole… …   Wikipedia

  • Gödel's incompleteness theorems — In mathematical logic, Gödel s incompleteness theorems, proved by Kurt Gödel in 1931, are two theorems stating inherent limitations of all but the most trivial formal systems for arithmetic of mathematical interest. The theorems are of… …   Wikipedia

  • List of first-order theories — In mathematical logic, a first order theory is given by a set of axioms in somelanguage. This entry lists some of the more common examples used in model theory and some of their properties. PreliminariesFor every natural mathematical structure… …   Wikipedia

  • Windows Presentation Foundation — This subsystem is a part of .NET Framework 3.0 Developed by Microsoft, the Windows Presentation Foundation (or WPF) is a computer software graphical subsystem for rendering user interfaces in Windows based applications. WPF, previously known as… …   Wikipedia

  • First-order logic — is a formal logical system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic (a less… …   Wikipedia

  • Mathematical logic — (also known as symbolic logic) is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic.[1] The field includes both the mathematical study of logic and the… …   Wikipedia

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