3
votes
0answers
112 views

Why the choice of pairing function in Subsystems of Second Order Arithmetic?

Simpson's book uses a pairing function $\langle i,j\rangle = (i+j)^2+j$. Is that choice of function simply unimportant, or does it have expository advantages over the Cantor pairing, or does it have ...
5
votes
2answers
390 views

Subscript 0 in Reverse Mathematics

What does the subscript 0 mean on terms like $\mathsf{ATR}_0$? Does it mean the same thing in $\Pi^1_k\text{-}\mathsf{CA}_0$? If I frame higher order analogues of these, should I change that ...
2
votes
0answers
70 views

Seeking name for an order raising operator in Higher Order Arithmetic.

Any class $X$ of order $j$ in HOA is in bijection with the order $j+1$ class built up from singletons $\{x\}$ of natural numbers $x$ just the way that $X$ is built up from the numbers $x$. And of ...
3
votes
1answer
486 views

Feferman's extensional and intensional applications of the method of arithmetization

At the very beginning of Feferman's Arithmetization of metamathematics in a general setting it can be read: The method of arithmetization, as developed by Gödel[10], exploits the possibility of ...