Abstract
The chapter surveys several important theoretical results in first-order logic. In Sect. 12.1 we prove that validity in first-order logic is undecidable, a result first proved by Alonzo Church. Validity is decidable for several classes of formulas defined by syntactic restrictions on their form (Sect. 12.2). Next, we introduce model theory (Sect. 12.3): the fact that a semantic tableau has a countable number of nodes leads to some interesting results. Finally, Sect. 12.4 contains an overview of Gödel’s surprising incompleteness result.
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Ben-Ari, M. (2012). First-Order Logic: Undecidability and Model Theory *. In: Mathematical Logic for Computer Science. Springer, London. https://doi.org/10.1007/978-1-4471-4129-7_12
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DOI: https://doi.org/10.1007/978-1-4471-4129-7_12
Publisher Name: Springer, London
Print ISBN: 978-1-4471-4128-0
Online ISBN: 978-1-4471-4129-7
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