Anagram & Information om | Engelska ordet PEANO

Exempel på hur man kan använda PEANO i en mening

• Presburger arithmetic is much weaker than Peano arithmetic, which includes both addition and multiplication operations.
• In mainstream mathematics, the axioms and the inference rules are commonly left implicit, and, in this case, they are almost always those of Zermelo–Fraenkel set theory with the axiom of choice (ZFC), or of a less powerful theory, such as Peano arithmetic.
• Though he was largely ignored during his lifetime, Giuseppe Peano (1858–1932), Bertrand Russell (1872–1970), and, to some extent, Ludwig Wittgenstein (1889–1951) introduced his work to later generations of philosophers.
• Laurence Kirby and Jeff Paris showed that it is unprovable in Peano arithmetic (but it can be proven in stronger systems, such as second-order arithmetic or Zermelo-Fraenkel set theory).
• Hilbert's statement is sometimes misunderstood, because by the "arithmetical axioms" he did not mean a system equivalent to Peano arithmetic, but a stronger system with a second-order completeness axiom.
• In Peano arithmetic, second-order arithmetic and related systems, and indeed in most (not necessarily formal) mathematical treatments of the well-ordering principle, the principle is derived from the principle of mathematical induction, which is itself taken as basic.
• For example, a machine that could solve the halting problem would be a hypercomputer; so too would one that could correctly evaluate every statement in Peano arithmetic.
• Although the formalisation of logic was much advanced by the work of such figures as Gottlob Frege, Giuseppe Peano, Bertrand Russell, and Richard Dedekind, the story of modern proof theory is often seen as being established by David Hilbert, who initiated what is called Hilbert's program in the Foundations of Mathematics.
• The arithmetical hierarchy is important in computability theory, effective descriptive set theory, and the study of formal theories such as Peano arithmetic.
• Interlingua de Peano, a controlled language of Neo Latin used as an auxiliary language - not to be confused with Interlingua de IALA (IA), a constructed language.
• Bertrand Russell and Alfred North Whitehead championed this programme, initiated by Gottlob Frege and subsequently developed by Richard Dedekind and Giuseppe Peano.
• Because Giuseppe Peano (1858–1932) was the first to discover one, space-filling curves in the 2-dimensional plane are sometimes called Peano curves, but that phrase also refers to the Peano curve, the specific example of a space-filling curve found by Peano.
• System T extends the simply typed lambda calculus with a type of natural numbers and higher-order primitive recursion; in this system all functions provably recursive in Peano arithmetic are definable.
• Latino sine flexione ("Latin without inflections"), Interlingua de Academia pro Interlingua (IL de ApI) or Peano's Interlingua (abbreviated as IL) is an international auxiliary language compiled by the Academia pro Interlingua under the chairmanship of the Italian mathematician Giuseppe Peano (1858–1932) from 1887 until 1914.
• Another strengthening of the theorem, in which existence of the permuted mixed partial is asserted, was provided by Peano in a short 1890 note on Mathesis:.
• It is notable that Skolem, like Löwenheim, wrote on mathematical logic and set theory employing the notation of his fellow pioneering model theorists Charles Sanders Peirce and Ernst Schröder, including Π, Σ as variable-binding quantifiers, in contrast to the notations of Peano, Principia Mathematica, and Principles of Mathematical Logic.
• There is no complete, consistent extension of even Peano arithmetic based on a computably enumerable set of axioms.
• As a consequence many theories, including Peano arithmetic, which cannot be properly axiomatised in finitary logic, can be in a suitable infinitary logic.
• In particular, Jensen proved the consistency of NFU relative to Peano arithmetic; meanwhile, the consistency of NF relative to anything remains an open problem, pending verification of Holmes's proof of its consistency relative to ZF.
• Q is finitely axiomatizable because it lacks Peano arithmetic's axiom schema of induction; nevertheless Q, like Peano arithmetic, is incomplete and undecidable in the sense of Gödel.

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