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27 relations: Algebraic structure, Axiom of adjunction, Decidability (logic), Diagonal lemma, Diophantine set, Edward Nelson, Elementary function arithmetic, Equiconsistency, Gödel's incompleteness theorems, Gödel's β function, General set theory, Gentzen's consistency proof, George Boolos, Kleene's T predicate, List of first-order theories, Peano axioms, Presburger arithmetic, Proof sketch for Gödel's first incompleteness theorem, Q (disambiguation), Raphael M. Robinson, Reverse mathematics, Second-order arithmetic, Self-verifying theories, Skolem arithmetic, Tarski's axioms, Ultrafinitism, Zermelo–Fraenkel set theory.
Algebraic structure
In mathematics, and more specifically in abstract algebra, an algebraic structure on a set A (called carrier set or underlying set) is a collection of finitary operations on A; the set A with this structure is also called an algebra.
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Axiom of adjunction
In mathematical set theory, the axiom of adjunction states that for any two sets x, y there is a set w.
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Decidability (logic)
In logic, the term decidable refers to the decision problem, the question of the existence of an effective method for determining membership in a set of formulas, or, more precisely, an algorithm that can and will return a boolean true or false value that is correct (instead of looping indefinitely, crashing, returning "don't know" or returning a wrong answer).
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Diagonal lemma
In mathematical logic, the diagonal lemma or fixed point theorem establishes the existence of self-referential sentences in certain formal theories of the natural numbers—specifically those theories that are strong enough to represent all computable functions.
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Diophantine set
In mathematics, a Diophantine equation is an equation of the form P(x1,..., xj, y1,..., yk).
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Edward Nelson
Edward Nelson (May 4, 1932 – September 10, 2014) was a professor in the Mathematics Department at Princeton University.
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Elementary function arithmetic
In proof theory, a branch of mathematical logic, elementary function arithmetic, also called EFA, elementary arithmetic and exponential function arithmetic, is the system of arithmetic with the usual elementary properties of 0, 1, +, ×, xy, together with induction for formulas with bounded quantifiers.
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Equiconsistency
In mathematical logic, two theories are equiconsistent if the consistency of one theory implies the consistency of the other theory, and vice versa.
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Gödel's incompleteness theorems
Gödel's incompleteness theorems are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system containing basic arithmetic.
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Gödel's β function
In mathematical logic, Gödel's β function is a function used to permit quantification over finite sequences of natural numbers in formal theories of arithmetic.
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General set theory
General set theory (GST) is George Boolos's (1998) name for a fragment of the axiomatic set theory Z. GST is sufficient for all mathematics not requiring infinite sets, and is the weakest known set theory whose theorems include the Peano axioms.
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Gentzen's consistency proof
Gentzen's consistency proof is a result of proof theory in mathematical logic, published by Gerhard Gentzen in 1936.
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George Boolos
George Stephen Boolos (September 4, 1940 – May 27, 1996) was an American philosopher and a mathematical logician who taught at the Massachusetts Institute of Technology.
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Kleene's T predicate
In computability theory, the T predicate, first studied by mathematician Stephen Cole Kleene, is a particular set of triples of natural numbers that is used to represent computable functions within formal theories of arithmetic.
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List of first-order theories
In mathematical logic, a first-order theory is given by a set of axioms in some language.
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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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Presburger arithmetic
Presburger arithmetic is the first-order theory of the natural numbers with addition, named in honor of Mojżesz Presburger, who introduced it in 1929.
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Proof sketch for Gödel's first incompleteness theorem
This article gives a sketch of a proof of Gödel's first incompleteness theorem.
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Q (disambiguation)
Q is the seventeenth letter of the English alphabet.
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Raphael M. Robinson
Raphael Mitchel Robinson (November 2, 1911 – January 27, 1995) was an American mathematician.
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Reverse mathematics
Reverse mathematics is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics.
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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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Self-verifying theories
Self-verifying theories are consistent first-order systems of arithmetic much weaker than Peano arithmetic that are capable of proving their own consistency.
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Skolem arithmetic
Skolem arithmetic is the first-order theory of the natural numbers with multiplication, named in honor of Thoralf Skolem.
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Tarski's axioms
Tarski's axioms, due to Alfred Tarski, are an axiom set for the substantial fragment of Euclidean geometry, called "elementary," that is formulable in first-order logic with identity, and requiring no set theory.
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Ultrafinitism
In the philosophy of mathematics, ultrafinitism, also known as ultraintuitionism, strict-finitism, actualism, and strong-finitism, is a form of finitism.
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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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Q arithmetic, Robinson Arithmetic, Robinson arithmetic Q, Robinson axioms, Robinson's Arithmetic, Robinson's Q.
References
[1] https://en.wikipedia.org/wiki/Robinson_arithmetic
