Primitive Recursive Arithmetic Quantification (6 results)

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! Primitive recursive arithmetic, or PRA, is a quantifier-free formalization of the natural numbers. It was first proposed by Skolem as a formalization of his finitist conception of the foundations of arithmetic, and it is widely agreed that all reasoning of PRA is finitist. Many also believe that all of finitism is captured by PRA, but others believe finitism can be extended to forms of recursion beyond primitive recursion, up to 0, which is the proof-theoretic ordinal of Peano arithmetic. PRA's proof theoretic ordinal is , where is the smallest transfinite ordinal. PRA is sometimes called Skolem arithmetic.

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! The primitive recursive functions are defined using primitive recursion and composition as central operations and are a strict subset of the recursive functions. The term was coined by Rózsa Péter. In computability theory, primitive recursive functions are a class of functions which form an important building block on the way to a full formalization of computability. These functions are also important in proof theory. Most of the functions normally studied in number theory are primitive recursive. For example: addition, division, factorial, exponential and the nth prime are all primitive recursive. So are many approximations to real-valued functions. In fact, it is difficult to devise a function that is not primitive recursive, although some are known. The set of primitive recursive functions is known as PR in complexity theory. Every primitive recursive function is a general recursive function.

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! Primitive recursive arithmetic, or PRA, is a quantifier-free formalization of the natural numbers. It was first proposed by Skolem as a formalization of his finitist conception of the foundations of arithmetic, and it is widely agreed that all reasoning of PRA is finitist. Many also believe that all of finitism is captured by PRA, but others believe finitism can be extended to forms of recursion beyond primitive recursion, up to 0, which is the proof-theoretic ordinal of Peano arithmetic. PRA's proof theoretic ordinal is , where is the smallest transfinite ordinal. PRA is sometimes called Skolem arithmetic. The language of PRA can express arithmetic propositions involving natural numbers and any primitive recursive function, including the operations of addition, multiplication, and exponentiation. PRA cannot explicitly quantify over the domain of natural numbers. PRA is often taken as the basic metamathematical formal system for proof theory, in particular for consistency proofs such as Gentzen's consistency proof of first-order arithmetic.

Taschenbuch. Condition: Neu. Primitive Recursive Arithmetic | Quantification, Thoralf Skolem, Finitism, Foundations of Mathematics, Ordinal Analysis, Peano Axioms, Natural Number, Primitive Recursive Function, Addition | Lambert M. Surhone (u. a.) | Taschenbuch | Englisch | 2026 | OmniScriptum | EAN 9786130346744 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu Print on Demand.

Taschenbuch. Condition: Neu. Primitive Recursive Function | Primitive Recursive Function, Primitive Recursive Arithmetic, Quantification, Thoralf Skolem, Finitism, Foundations of Mathematics, Ordinal Analysis, Peano Axioms, Natural Number | Lambert M. Surhone (u. a.) | Taschenbuch | Englisch | 2026 | OmniScriptum | EAN 9786130341992 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu Print on Demand.

Taschenbuch. Condition: Neu. Primitive Recursive Arithmetic | Primitive Recursive Arithmetic, Quantification, Thoralf Skolem, Finitism, Foundations of Mathematics, Ordinal Analysis, Peano Axioms, Natural Number | Lambert M. Surhone (u. a.) | Taschenbuch | Englisch | 2026 | OmniScriptum | EAN 9786130341916 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu Print on Demand.