Thursday, February 22, 2001
An argument. (Lecture).
An axiom of a consistent axioms system is independent if its negation together with the remaining axioms is still consistent. Another way to say this is that the axiom cannot be proved from the other axioms. (Lecture).
Yes. One can present models for Non-Euclidean geometries. (Lecture).
In the 19th century: 1888 by Dedekind, and 1889 by Peano. (Lecture).
Yes in both cases. (Lecture).