### Some articles on *partial recursive function, recursive function, recursive, recursive functions, functions*:

Counter Machine Models - The Models in More Detail - 1961: Minsky's Model of A

... led Minsky to the following definition of "an interesting basis for

**Partial Recursive Function**Reduced To A "program" of Only Two Instructions... led Minsky to the following definition of "an interesting basis for

**recursive function**theory involving programs of only the simplest arithmetic operations" (Minsky (1961) p ... His "Theorem Ia" asserts that any**partial recursive function**is represented by "a program operating on two integers S1 and S2 using instructions Ij of the forms (cf ... theorem is the context of a second "Theorem IIa" that "...represents any**partial recursive function**by a program operating on one integer S using instructions Ij ...Recursively Enumerable Set - Equivalent Formulations

... That is, S is the domain (co-range) of a

... That is, S is the domain (co-range) of a

**partial recursive function**... There is a**partial recursive function**f such that Enumerability The set S is the range of a**partial recursive function**... The set S is the range of a total**recursive function**or empty ...Adequate Pointclass

... field of descriptive set theory, a pointclass can be called adequate if it contains all

... field of descriptive set theory, a pointclass can be called adequate if it contains all

**recursive**pointsets and is closed under**recursive**substitution, bounded universal and existential quantification and ...Tennenbaum's Theorem - Recursive Structures For PA

... A structure in the language of PA is

... A structure in the language of PA is

**recursive**if there are**recursive functions**+ and × from to, a**recursive**two-place relation < on, and distinguished constants such that where ... the isomorphism must be a bijection, every**recursive**model is countable ...

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### Famous quotes containing the words function and/or partial:

“Think of the tools in a tool-box: there is a hammer, pliers, a saw, a screwdriver, a rule, a glue-pot, nails and screws.—The *function* of words are as diverse as the functions of these objects.”

—Ludwig Wittgenstein (1889–1951)

“Both the man of science and the man of art live always at the edge of mystery, surrounded by it. Both, as a measure of their creation, have always had to do with the harmonization of what is new with what is familiar, with the balance between novelty and synthesis, with the struggle to make *partial* order in total chaos.... This cannot be an easy life.”

—J. Robert Oppenheimer (1904–1967)

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