The initial goal of the present paper is to reveal a mistake committed by Hintikka in a recent paper on the foundations of mathematics. His claim that independence-friendly logic (IFL) is the real ...

From these nine axioms, one can derive all of mathematics. These provide the foundation of mathematics, a field that you can likely tell that I love dearly.” ...

Vladimir Voevodsky’s univalent foundations program aims to rebuild mathematics in a way that will allow computers to check all mathematical proofs. Voevodsky followed Makkai’s path but used ...

If so, the argument went, the very foundations of mathematics would be flawed, and the entire subject would collapse like a house of cards. As mathematicians determined in the 1960s, however, that ...