Abstract
A first-order property of a structure is a property that can be expressed in first-order logic. Some important properties are first-order but many are not. We will see why finiteness, minimality, order-minimality, and being well ordered are not first-order, and how some such properties can be expressed in higher-order logics.
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Notes
- 1.
A theory is a set of first-order sentences.
References
Knight, J. F., Pillay, A., & Steinhorn, C. (1986). Definable sets in ordered structures. II. Transactions of the American Mathematical Society, 295(2), 593–605.
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Kossak, R. (2018). First-Order Properties. In: Mathematical Logic. Springer Graduate Texts in Philosophy, vol 3. Springer, Cham. https://doi.org/10.1007/978-3-319-97298-5_14
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DOI: https://doi.org/10.1007/978-3-319-97298-5_14
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