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First-order logic

In Handbook of mathematical logic. New York: North-Holland (1977)

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  1. Mathematizing as a virtuous practice: different narratives and their consequences for mathematics education and society.Deborah Kant & Deniz Sarikaya - 2020 - Synthese 199 (1-2):3405-3429.
    There are different narratives on mathematics as part of our world, some of which are more appropriate than others. Such narratives might be of the form ‘Mathematics is useful’, ‘Mathematics is beautiful’, or ‘Mathematicians aim at theorem-credit’. These narratives play a crucial role in mathematics education and in society as they are influencing people’s willingness to engage with the subject or the way they interpret mathematical results in relation to real-world questions; the latter yielding important normative considerations. Our strategy is (...)
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  • On the mathematical and foundational significance of the uncountable.Dag Normann & Sam Sanders - 2019 - Journal of Mathematical Logic 19 (1):1950001.
    We study the logical and computational properties of basic theorems of uncountable mathematics, including the Cousin and Lindelöf lemma published in 1895 and 1903. Historically, these lemmas were among the first formulations of open-cover compactness and the Lindelöf property, respectively. These notions are of great conceptual importance: the former is commonly viewed as a way of treating uncountable sets like e.g. [Formula: see text] as “almost finite”, while the latter allows one to treat uncountable sets like e.g. [Formula: see text] (...)
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  • (1 other version)Zum Aufbau Einer Mehrsortigen Elementaren Logik.Heinz Kaphengst - 1985 - Mathematical Logic Quarterly 31 (1‐6):39-56.
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  • Social logics and expert systems.Giorgio Sacchi - 1994 - AI and Society 8 (1):84-87.
    My goal is to emphasize the way we generally use the word ‘logic’ and the sort of problems related to the definition of logic and the sort of problems related to the definition of logic. I also wish to underline the differences between human intelligence and artificial intelligence.
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  • A model-theoretic approach to ordinal analysis.Jeremy Avigad & Richard Sommer - 1997 - Bulletin of Symbolic Logic 3 (1):17-52.
    We describe a model-theoretic approach to ordinal analysis via the finite combinatorial notion of an α-large set of natural numbers. In contrast to syntactic approaches that use cut elimination, this approach involves constructing finite sets of numbers with combinatorial properties that, in nonstandard instances, give rise to models of the theory being analyzed. This method is applied to obtain ordinal analyses of a number of interesting subsystems of first- and second-order arithmetic.
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