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Order‐free Recursion on the Real Numbers
Author(s) -
Brattka Vasco
Publication year - 1997
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19970430206
Subject(s) - recursion (computer science) , mathematics , primitive recursive function , μ operator , class (philosophy) , order (exchange) , limit (mathematics) , computable number , real analysis , computable function , computable analysis , algebra over a field , discrete mathematics , recursive functions , pure mathematics , algorithm , computer science , mathematical analysis , finance , artificial intelligence , economics
We investigate operations, computable in the sense of Recursive Analysis, which can be generated recursively from the arithmetic operations and the limit operation without using any tests on the real numbers. These functions, called order‐free recursive, can be shown to include a large class of computable functions. As main tools we provide an effective version of the Stone‐Weierstraß Approximation Theorem, as well as recursive partitions of unity.