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1. A Framework for Metamathematics

  • 2022
  • OriginalPaper
  • Chapter
Published in:
Author
Lorenz Halbeisen
Published in
Axiomatic Thinking II
Publisher
Springer International Publishing

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Abstract

The chapter 'A Framework for Metamathematics' delves into the evolution of Hilbert’s Program, which shifted the focus from the inherent truth of axioms to their consistency. This paradigm shift allowed for the investigation of any consistent axiomatic system, not just those relevant to actual mathematics. The text explores the non-constructive principles essential for metamathematics, such as finiteness, potentially infinite sets, and the law of excluded middle. It highlights the construction of models for various axiomatic systems, including standard and non-standard models of real numbers. The chapter concludes by proposing a view of mathematics as the investigation of formal axiomatic systems, free from ideological constraints, and emphasizes the freedom and flexibility this approach offers.
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next chapter Simplified Cut Elimination for Kripke-Platek Set Theory
Title
A Framework for Metamathematics
Author
Lorenz Halbeisen
Copyright Year
2022
Book
Axiomatic Thinking II

Print ISBN: 978-3-030-77798-2

Electronic ISBN: 978-3-030-77799-9

Copyright Year: 2022

DOI
https://doi.org/10.1007/978-3-030-77799-9_1
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