I have been told that constructivist/intuitionist logic is classical logic - LEM.
I see why LEM doesn't hold given the basic philosophy of constructivist mathematics, ehich I understand to be based on the interpretation of $\exists$ as "we can construct" (and a similar interpretation of the other logical symbols).
However, is it also true that if we take LEM as an additional axiom, and "append" it to whatever mathematical theory we are working with, can we then reproduce any classical proof within the constructivist interpretation?
This is not at all obvious to me from the "philosophical" explanation of what constructivist math is about.
Not that there are two questions:
is any theorem that is provable in classical math also provable in constructivist math + LEM?
is any classical proof also reproducable as a constrictivist proof with the same logical steps, within the same theory but with LEM appended as an axiom?
I don't know the answer to either but my question is about the latter.