With regards to the axiom of choice, I see it as a necessary part of a logical framework. Without AC some well-behavedness properties of logic do not hold. For example, skolemization can not be done in-logic in the general case and Schröder-Bernstein theorem does not hold, so cardinalities can not be proved to form a total order.
This does not preclude study of a system without AC. One can study any logic (including one without AC) with a suitable embedding. On 11/03/18 11:53, Mario Xerxes Castelán Castro wrote: > By the way, the _definite_ description operator is also called > “Russell's operator” or “Russell’s iota” > (http://us.metamath.org/mpegif/df-iota.html”.
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