What were the earliest “unpleasant” consequences of the Axiom of Choice (and its negation) to be deduced?
Was the idea of encoding meta-mathematics into arithmetic in the air when Gödel proved incompleteness theorems?
In which article/book chapter did Cantor, Hilbert, and Poincaré formally define or directly discusse the term “potential infinity”?
Did Gödel consider himself primarily a philosopher who is interested in mathematics (instead of the other way round)?
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