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21 relations: Arithmetical hierarchy, Axiom schema of predicative separation, Computability theory, Constructive set theory, Context-sensitive grammar, ELEMENTARY, Impredicativity, Kripke–Platek set theory, Lévy hierarchy, Mathematical logic, Peano axioms, Polynomial hierarchy, Primitive recursive function, Second-order arithmetic, Sentence (mathematical logic), Subtyping, System F, System F-sub, Type theory, Typed lambda calculus, Zermelo–Fraenkel set theory.
Arithmetical hierarchy
In mathematical logic, the arithmetical hierarchy, arithmetic hierarchy or Kleene–Mostowski hierarchy classifies certain sets based on the complexity of formulas that define them.
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Axiom schema of predicative separation
In axiomatic set theory, the axiom schema of predicative separation, or of restricted, or Δ0 separation, is a schema of axioms which is a restriction of the usual axiom schema of separation in Zermelo–Fraenkel set theory.
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Computability theory
Computability theory, also known as recursion theory, is a branch of mathematical logic, of computer science, and of the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees.
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Constructive set theory
Constructive set theory is an approach to mathematical constructivism following the program of axiomatic set theory.
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Context-sensitive grammar
A context-sensitive grammar (CSG) is a formal grammar in which the left-hand sides and right-hand sides of any production rules may be surrounded by a context of terminal and nonterminal symbols.
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ELEMENTARY
In computational complexity theory, the complexity class ELEMENTARY of elementary recursive functions is the union of the classes The name was coined by László Kalmár, in the context of recursive functions and undecidability; most problems in it are far from elementary.
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Impredicativity
Something that is impredicative, in mathematics and logic, is a self-referencing definition.
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Kripke–Platek set theory
The Kripke–Platek axioms of set theory (KP), pronounced, are a system of axiomatic set theory developed by Saul Kripke and Richard Platek.
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Lévy hierarchy
In set theory and mathematical logic, the Lévy hierarchy, introduced by Azriel Lévy in 1965, is a hierarchy of formulas in the formal language of the Zermelo–Fraenkel set theory, which is typically called just the language of set theory.
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Mathematical logic
Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics.
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Peano axioms
In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano.
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Polynomial hierarchy
In computational complexity theory, the polynomial hierarchy (sometimes called the polynomial-time hierarchy) is a hierarchy of complexity classes that generalize the classes P, NP and co-NP to oracle machines.
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Primitive recursive function
In computability theory, primitive recursive functions are a class of functions that are defined using primitive recursion and composition as central operations and are a strict subset of the total µ-recursive functions (µ-recursive functions are also called partial recursive).
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Second-order arithmetic
In mathematical logic, second-order arithmetic is a collection of axiomatic systems that formalize the natural numbers and their subsets.
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Sentence (mathematical logic)
In mathematical logic, a sentence of a predicate logic is a boolean-valued well-formed formula with no free variables.
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Subtyping
In programming language theory, subtyping (also subtype polymorphism or inclusion polymorphism) is a form of type polymorphism in which a subtype is a datatype that is related to another datatype (the supertype) by some notion of substitutability, meaning that program elements, typically subroutines or functions, written to operate on elements of the supertype can also operate on elements of the subtype.
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System F
System F, also known as the (Girard–Reynolds) polymorphic lambda calculus or the second-order lambda calculus, is a typed lambda calculus that differs from the simply typed lambda calculus by the introduction of a mechanism of universal quantification over types.
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System F-sub
In the branch of mathematical logic known as type theory, System F<:, pronounced "F-sub", is an extension of system F with subtyping.
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Type theory
In mathematics, logic, and computer science, a type theory is any of a class of formal systems, some of which can serve as alternatives to set theory as a foundation for all mathematics.
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Typed lambda calculus
A typed lambda calculus is a typed formalism that uses the lambda-symbol (\lambda) to denote anonymous function abstraction.
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Zermelo–Fraenkel set theory
In mathematics, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox.
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References
[1] https://en.wikipedia.org/wiki/Bounded_quantifier
