Abstract
In this final chapter we present some results, due to Lindström [25], which we have already mentioned several times. They show that first-order logic occupies a unique place among logical systems. Indeed, we shall prove:
-
(a)
There is no logical system with more expressive power than first-order logic, for which both the Compactness Theorem and the Löwenheim-Skolem Theorem hold (Section 3).
-
(b)
There is no logical system with more expressive power than first-order logic, for which the Löwenheim-Skolem Theorem holds and for which the set of valid sentences is enumerable (Section 4).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media New York
About this chapter
Cite this chapter
Ebbinghaus, HD., Flum, J., Thomas, W. (1994). Lindström’s Theorems. In: Mathematical Logic. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2355-7_13
Download citation
DOI: https://doi.org/10.1007/978-1-4757-2355-7_13
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-2357-1
Online ISBN: 978-1-4757-2355-7
eBook Packages: Springer Book Archive