For all you first order/predicate logic fans out there

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From The Annotated Turing: now reached page 226 and it is still good.

I think Charles Petzold has made a mistake – has he? Please read on and let me know.

Three axioms from Hilbert and Bernays

Petzold says these three axioms come from Hilbert and Bernays and they mean:

  1. Every member has a successor
  2. There exists a number that does not have a successor
  3. That is r is a successor  to x and y and x is the successor to s, then y is also the successor to s.

But surely the second axiom actually means there exists an x which is not a successor of y?

Comments please.

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2 thoughts on “For all you first order/predicate logic fans out there”

  1. Pingback: Gödel, Turing and decidability | cartesian product

  2. The second statement should read “there exists a number which does not have a predecessor”, this is what we call zero.

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