Re: Real mathematics vs FOL

biubo wrote:
I have two questions:

1)Can you show me some mathematical results which cannot be translated into first order logic?

2) I remember that once I read on a book of Ebbinghaus, Flum, Thomas that in f.o. logic you can not define the concept of torsion group.
Is the theory of torsion groups out of the scope of FOL ?

It would be helpful if you could give some ideas as to what you
think "real mathematics" should be.


Thank you.




--
-----------------------------------------------------

What we call 'I' is just a swinging door which moves
when we inhale and exhale.
Shunryu Suzuki
----------------------------------------------------
.

Relevant Pages

  • Re: Real mathematics vs FOL
    ... biubo wrote: ... logic you can not define the concept of torsion group. ... Is the theory of torsion groups out of the scope of FOL? ... the common mathematics, the one that you can do without knowing much about logic. ...
    (sci.logic)
  • Re: Real mathematics vs FOL
    ... The Axiom of Separation in Z-F set theory cannot be expressed in FOL. ... logic you can not define the concept of torsion group. ... think "real mathematics" should be. ...
    (sci.logic)
  • Re: Real mathematics vs FOL
    ... I remember that once I read on a book of Ebbinghaus, Flum, Thomas ... logic you can not define the concept of torsion group. ... Is the theory of torsion groups out of the scope of FOL? ... think "real mathematics" should be. ...
    (sci.logic)
  • Re: Real mathematics vs FOL
    ... I remember that once I read on a book of Ebbinghaus, Flum, Thomas that ... logic you can not define the concept of torsion group. ... think "real mathematics" should be. ... the one that you can do without knowing much about ...
    (sci.logic)
Quantcast