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In page Alfred Tarski:
"This publication set out the modern model-theoretic definition of (semantic) logical consequence, or at least the basis for it. Whether Tarski's notion was entirely the modern one turns on whether he intended to admit models with varying domains (and in particular, models with domains of different cardinalities).[citation needed] This question is a matter of some debate in the philosophical literature. John Etchemendy stimulated much of the discussion about Tarski's treatment of varying domains.[2]
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