Abstract
It follows from Gödel's Completeness Theorem that a theory is consistent if and only if it has a model. In particular, the consistency of Peano Arithmetic follows from \(\mathbb{N} \models \mathbf{PA}\).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Halbeisen, L., Krapf, R. (2020). The Second Incompleteness Theorem. In: Gödel's Theorems and Zermelo's Axioms. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-52279-7_11
Download citation
DOI: https://doi.org/10.1007/978-3-030-52279-7_11
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-52278-0
Online ISBN: 978-3-030-52279-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)