All Questions

At the end of the paper Division by three by Peter G. Doyle and John H. Conway, the authors say: Not that we believe there really are any such things as infinite sets, or that the Zermelo-Fraenkel ...

As you all know, Ronald Graham just passed away. He is famous for many fabulous contributions to finite combinatorics, and much much more, but perhaps none of them is as popular as the infamous ...

Consider a 2-sorted first-order logic with equality (for first-sort entities). The first sort consists of numbers, the second sort (which will be capitalized) of unary functions. There is one constant,...

I will ask the question first and then explain. QUESTION: FPA can prove its own consistency in the Godelian sense. But can it really prove its consistency? FPA is a multi-sorted first-order theory,...

Hilbert's program is popularly understood as an attempt to justify infinitary mathematics with a finitary consistency proof. Godel's Second Theorem is usually considered as showing this is not ...

Consider second-order Peano Arithmetic Z2, i.e. the two-sorted first-order theory with induction and comprehension. Remove the assumption about the totality of the successor relationship (the ...