Abstract
A first-order property of a structure is a property that can be expressed by a formula of first-order logic. Many properties are first-order but some important ones 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.
Recall that a theory is any set of first-order sentences.
References
Knight, J. F., Anand P., & 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. (2024). First-Order Properties. In: Mathematical Logic. Springer Graduate Texts in Philosophy, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-031-56215-0_14
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DOI: https://doi.org/10.1007/978-3-031-56215-0_14
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