- arithmetical set
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A set of natural numbers that can be defined by a formula of first-order Peano arithmetic.Syn: arithmetic set
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arithmetical set
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Arithmetical set — In mathematical logic, an arithmetical set (or arithmetic set) is a set of natural numbers that can be defined by a formula of first order Peano arithmetic. The arithmetical sets are classified by the arithmetical hierarchy.A function f:subseteq… … Wikipedia
Arithmetical hierarchy — In mathematical logic, the arithmetical hierarchy, arithmetic hierarchy or Kleene hierarchy classifies certain sets based on the complexity of formulas that define them. Any set that receives a classification is called arithmetical. The… … Wikipedia
Arithmetical complement of a number — Complement Com ple*ment, n. [L. complementun: cf. F. compl[ e]ment. See {Complete}, v. t., and cf. {Compliment}.] 1. That which fills up or completes; the quantity or number required to fill a thing or make it complete. [1913 Webster] 2. That… … The Collaborative International Dictionary of English
Arithmetical compliment of a logarithm — Complement Com ple*ment, n. [L. complementun: cf. F. compl[ e]ment. See {Complete}, v. t., and cf. {Compliment}.] 1. That which fills up or completes; the quantity or number required to fill a thing or make it complete. [1913 Webster] 2. That… … The Collaborative International Dictionary of English
Set-theoretic definition of natural numbers — Several ways have been proposed to define the natural numbers using set theory.The contemporary standardIn standard (ZF) set theory the natural numbersare defined recursively by 0 = {} (the empty set) and n +1 = n ∪ { n }. Then n = {0,1,..., n… … Wikipedia
Definable set — In mathematical logic, a definable set is an n ary relation on the domain of a structure whose elements are precisely those elements satisfying some formula in the language of that structure. A set can be defined with or without parameters, which … Wikipedia
Recursively 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… … Wikipedia
Zermelo–Fraenkel set theory — Zermelo–Fraenkel set theory, with the axiom of choice, commonly abbreviated ZFC, is the standard form of axiomatic set theory and as such is the most common foundation of mathematics.ZFC consists of a single primitive ontological notion, that of… … Wikipedia
Recursive set — In computability theory, a set of natural numbers is called recursive, computable or decidable if there is an algorithm which terminates after a finite amount of time and correctly decides whether or not a given number belongs to the set. A more… … Wikipedia
Kripke–Platek set theory — The Kripke–Platek axioms of set theory (KP) (IPAEng|ˈkrɪpki ˈplɑːtɛk) are a system of axioms of axiomatic set theory, developed by Saul Kripke and Richard Platek. The axiom system is written in first order logic; it has an infinite number of… … Wikipedia
