finite hierarchy
71Recursively enumerable set — In computability theory, traditionally called recursion theory, a set S of natural numbers is called recursively enumerable, computably enumerable, semidecidable, provable or Turing recognizable if: There is an algorithm such that the set of… …
72Second-order logic — In logic and mathematics second order logic is an extension of first order logic, which itself is an extension of propositional logic.[1] Second order logic is in turn extended by higher order logic and type theory. First order logic uses only… …
73Machine that always halts — In computability theory, a machine that always halts also called a decider (Sipser, 1996) or a total Turing machine (Kozen, 1997) is a Turing machine that halts for every input. Because it always halts, the machine is able to decide whether a… …
74cosmos — /koz meuhs, mohs/, n., pl. cosmos, cosmoses for 2, 4. 1. the world or universe regarded as an orderly, harmonious system. 2. a complete, orderly, harmonious system. 3. order; harmony. 4. any composite plant of the genus Cosmos, of tropical… …
75logic, history of — Introduction the history of the discipline from its origins among the ancient Greeks to the present time. Origins of logic in the West Precursors of ancient logic There was a medieval tradition according to which the Greek philosopher …
76Algorithm — Flow chart of an algorithm (Euclid s algorithm) for calculating the greatest common divisor (g.c.d.) of two numbers a and b in locations named A and B. The algorithm proceeds by successive subtractions in two loops: IF the test B ≤ A yields yes… …
77Regular expression — In computing, a regular expression provides a concise and flexible means for matching (specifying and recognizing) strings of text, such as particular characters, words, or patterns of characters. Abbreviations for regular expression include… …
78Hyperreal number — *R redirects here. For R*, see Rockstar Games. The system of hyperreal numbers represents a rigorous method of treating the infinite and infinitesimal quantities. The hyperreals, or nonstandard reals, *R, are an extension of the real numbers R… …
79Rectangle — Family Orthotope Type Quadrilateral Edges and vertices 4 Schläfli symbol {}x{} …
80König's lemma — or König s infinity lemma is a theorem in graph theory due to Dénes Kőnig (1936). It gives a sufficient condition for an infinite graph to have an infinitely long path. The computability aspects of this theorem have been thoroughly investigated… …
