Abstract
The greater part of our exposition so far has been devoted to the development and investigation of first-order logic. We can justify the dominant role assumed by first-order logic in several ways:
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(a)
First-order logic is in principle sufficient for mathematics.
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(b)
The intuitive concept of proof and the consequence relation can be adequately described by a formal notion of proof, which is given by means of a calculus.
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(c)
A number of semantic results such as the Compactness Theorem or the Löwenheim-Skolem Theorem leads to an enrichment of mathematical methods.
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© 1994 Springer Science+Business Media New York
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Ebbinghaus, HD., Flum, J., Thomas, W. (1994). An Algebraic Characterization of Elementary Equivalence. In: Mathematical Logic. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2355-7_12
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DOI: https://doi.org/10.1007/978-1-4757-2355-7_12
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-2357-1
Online ISBN: 978-1-4757-2355-7
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