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As early as 1934, Popper wrote of the search for truth as "one of the strongest motives for scientific discovery." Still, he describes in Objective Knowledge (1972) early concerns about the much-criticised notion of truth as correspondence. Then came the semantic theory of truth formulated by the logician Alfred Tarski and published in 1933. Popper writes of learning in 1935 of the consequences of Tarski's theory, to his intense joy. The theory met critical objections to truth as correspondence and thereby rehabilitated it. The theory also seemed, in Popper's eyes, to support metaphysical realism and the regulative idea of a search for truth.

What theory of interest to Popper did Alfred Tarski publish in 1933?
semantic theory of truth