[FOM] A question concerning incompleteness

Arnon Avron aa at tau.ac.il
Tue Jun 3 12:40:53 EDT 2014

Dear Fomers,

I have a question:

It is well-known that no consistent axiomatic extension
of Robinson's system Q or Shoenfield's system N
(from his great book "Mathematical Logic") can be complete.

Does this theorem remain true if we delete from Q
the axiom that states that every number different than 0
has a predecessor, or if we delete from N the axiom
that states that the relation < on the natural numbers
is linear?


Arnon Avron

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