Two-variable logic has weak, but not strong, Beth definability

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Journal of Symbolic Logic 86 (2):785-800 (2021)
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Abstract

We prove that the two-variable fragment of first-order logic has the weak Beth definability property. This makes the two-variable fragment a natural logic separating the weak and the strong Beth properties since it does not have the strong Beth definability property.

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10.1017/jsl.2021.7

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References found in this work

Model Theory.Michael Makkai, C. C. Chang & H. J. Keisler - 1991 - Journal of Symbolic Logic 56 (3):1096.
Language in action.Johan Benthem - 1991 - Journal of Philosophical Logic 20 (3):225 - 263.
Distances between formal theories.Michele Friend, Mohamed Khaled, Koen Lefever & Gergely Székely - unknown - Review of Symbolic Logic 13 (3):633-654.
On Weak and Strong Interpolation in Algebraic Logics.Gábor Sági & Saharon Shelah - 2006 - Journal of Symbolic Logic 71 (1):104 - 118.

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