Why the choice of pairing function in Subsystems of Second Order Arithmetic? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T02:02:43Z http://mathoverflow.net/feeds/question/115806 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/115806/why-the-choice-of-pairing-function-in-subsystems-of-second-order-arithmetic Why the choice of pairing function in Subsystems of Second Order Arithmetic? Colin McLarty 2012-12-08T16:36:50Z 2012-12-08T16:36:50Z <p>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 real advantages over the Cantor pairing in terms of quantifier complexity of proofs using it?</p>