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For question in Proof Theory, where "proofs" themselves are the object of mathematical investigation. It is not to be used to request a proof of some result.

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Is monotonicity redundant in this definition of Tarskian logics?

Given a logic over a language $L$, which has a consequence relation $\vdash$. This logic is Tarskian if for every $\Gamma \cup \Delta \cup {\alpha} \subseteq L$: If $\alpha \in \Gamma$, then $\Gamma …