- Peano arithmetic
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A set of axioms of first-order logic for the natural numbers specifying the operations of zero, successor, addition and multiplication, including a first-order schema of induction.
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Peano arithmetic
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Peano axioms — In mathematical logic, the Peano axioms, also known as the Dedekind Peano axioms or the Peano postulates, are a set of axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano. These axioms have been used… … Wikipedia
Peano-Arithmetik — Die Peano Arithmetik (erster Stufe) ist eine Theorie der Arithmetik, also der Natürlichen Zahlen, innerhalb der Prädikatenlogik erster Stufe. Als Axiome werden die Peano Axiome verwendet, wobei das Induktionsaxiom durch ein Axiomenschema ersetzt… … Deutsch Wikipedia
Peano , Giuseppe — (1858–1932) Italian mathematician and logician Peano, who was born at Spinetta near Cuneo, in Italy, studied at the University of Turin and was an assistant there from 1880. He became extraordinary professor of infinitesimal calculus in 1890 and… … Scientists
Non-standard model of arithmetic — In mathematical logic, a nonstandard model of arithmetic is a model of (first order) Peano arithmetic that contains nonstandard numbers. The standard model of arithmetic consists of the set of standard natural numbers {0, 1, 2, …}. The elements… … Wikipedia
Second-order arithmetic — In mathematical logic, second order arithmetic is a collection of axiomatic systems that formalize the natural numbers and sets thereof. It is an alternative to axiomatic set theory as a foundation for much, but not all, of mathematics. The… … Wikipedia
Non-standard arithmetic — In mathematical logic, a nonstandard model of arithmetic is a model of (first order) Peano arithmetic that contains nonstandard numbers. The standard model of arithmetic consists of the set of standard natural numbers {0, 1, 2, hellip;}. The… … Wikipedia
Robinson arithmetic — In mathematics, Robinson arithmetic, or Q, is a finitely axiomatized fragment of Peano arithmetic (PA), first set out in Robinson (1950). Q is essentially PA without the axiom schema of induction. Even though Q is much weaker than PA, it is still … Wikipedia
Presburger arithmetic — is the first order theory of the natural numbers with addition, named in honor of Mojżesz Presburger, who published it in 1929. It is not as powerful as Peano arithmetic because it omits multiplication.OverviewThe language of Presburger… … Wikipedia
Primitive recursive arithmetic — Primitive recursive arithmetic, or PRA, is a quantifier free formalization of the natural numbers. It was first proposed by Skolem [Thoralf Skolem (1923) The foundations of elementary arithmetic in Jean van Heijenoort, translator and ed. (1967)… … Wikipedia
Ordinal arithmetic — In the mathematical field of set theory, ordinal arithmetic describes the three usual operations on ordinal numbers: addition, multiplication, and exponentiation. Each can be defined in essentially two different ways: either by constructing an… … Wikipedia
