degree of definability
1Turing degree — Post s problem redirects here. For the other Post s problem , see Post s correspondence problem. In computer science and mathematical logic the Turing degree or degree of unsolvability of a set of natural numbers measures the level of algorithmic …
2Computability 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 …
3Recursion 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… …
4Structure (mathematical logic) — In universal algebra and in model theory, a structure consists of a set along with a collection of finitary operations and relations which are defined on it. Universal algebra studies structures that generalize the algebraic structures such as… …
5Pointclass — In the mathematical field of descriptive set theory, a pointclass is a collection of sets of points, where a point is ordinarily understood to be an element of some perfect Polish space. In practice, a pointclass is usually characterized by some… …
6Julia Robinson — Infobox Scientist name = Julia Hall Bowman Robinson box width = imagesize = 200px caption = Julia Robinson in 1975 birth date = December 8, 1919 birth place = St. Louis, Missouri, United States death date = July 30, 1985 death place = Oakland,… …
7Hyperarithmetical theory — In recursion theory, hyperarithmetic theory is a generalization of Turing computability. It has close connections with definability in second order arithmetic and with weak systems of set theory such as Kripke–Platek set theory. It is an… …
8Mathematical 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… …
9Post's theorem — In computability theory Post s theorem, named after Emil Post, describes the connection between the arithmetical hierarchy and the Turing degrees. Background The statement of Post s theorem requires several concepts relating to definability and… …
10mathematics, 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… …
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