TWO-VARIABLE LOGIC HAS WEAK, BUT NOT STRONG, BETH DEFINABILITY
HAJNAL ANDRÉKA, ISTVÁN NÉMETI · Journal of Symbolic Logic · 2021
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.