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Reflection Principles, Generic Large Cardinals, and the Continuum Problem Read chapter Read first chapter

2021 | OriginalPaper | Chapter

Irrational-Based Computability of Functions

Authors : Mariko Yasugi, Yoshiki Tsujii, Takakazu Mori

Published in: Advances in Mathematical Logic

Publisher: Springer Nature Singapore

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Abstract

We investigate a sort of a unifying theory of computability of real functions, continuous or discontinuous, called here “irrational-based” (IB-) computability. All the examples which are computable in our various theories presented previously are IB-computable. The basic requirements of computability, the sequential computability and the effective continuity, are defined relative to computable irrational real sequences. The family of IB-computable functions is closed under IB-effective convergence. In order to certify the fruitfulness of IB-computability, quite a number of examples are presented.

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previous chapter Choiceless Löwenheim–Skolem Property and Uniform Definability of Grounds
next chapter “Gaisi Takeuti’s Finitist Standpoint” and Its Mathematical Embodiment
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Metadata
Title
Irrational-Based Computability of Functions
Authors
Mariko Yasugi
Yoshiki Tsujii
Takakazu Mori
Copyright Year
2021
Publisher
Springer Nature Singapore
Book
Advances in Mathematical Logic

Print ISBN: 978-981-16-4172-5

Electronic ISBN: 978-981-16-4173-2

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-981-16-4173-2_9

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