Is this formula really the nine axioms?

Question

I was reading a note from guardian.uk called What lurks beneath a scientist's lab coat?, a little gallery of geeky-tattoos.

However, number 11 in the series has the following image and caption text:

'From these nine axioms,' writes Turing Eret, a software designer in Colarado, 'one can derive all of mathematics – a field you can likely tell that I love dearly'

Is that really so? Are those the nine axioms? (I guess it means the ZF axioms) If so, how are they expressed like that? (Last question meaning: how does that expression imply the nine axioms?)

I tried to search it around but searching formulas is really hard. Also, Google and TinEye image search wouldn't produce anything relevant.

I really suck at math but I love it, so forgive me if I'm asking something stupid.

Answer 1

It is called a Y combinator. This particular one was invented by Haskell Curry according to the Wikipedia page. It has little to do with set theory and I am not sure what are the "nine axioms" referred to. I know it as being a useful tool in constructing a LISP-like language from combinator calculus. It has the effect of applying its argument to itself, i.e. Yx -> x(Yx) -> x(x(Yx)), which can be used to implement recursion. This is not the only expression with such an effect; scroll down the Wikipedia page to see some other examples of Y combinators.

Answer 2

That's my arm! Yeah, it was incorrectly labelled in the Guardian article. That is the Y Combinator as others have mentioned. My OTHER tattoo are the ZFC axioms. In the book, both tattoos are pictured but only the ZFC one is described. A bit unfortunate, but oh well. What can you do?