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Answer by Farmer S for Does "agreement on cardinalities" imply second-order...

No, second order logic does not have the weak test property: let $\mathfrak{B}=(\mathbb{R},{<})$ (that is, the real numbers with the only predicate being the usual "less than" order) and let...

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Does "agreement on cardinalities" imply second-order elementary...

Say that a logic $\mathcal{L}$ satisfies the weak test property iff for all $\mathfrak{A}\subseteq\mathfrak{B}$ we have $(1)\implies(2)$ below:For each $\mathcal{L}$-formula $\varphi$ with parameters...

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