Re: A question about FOL theories and models

Nam Nguyen wrote:
ZF(C), after all, is just one theory out of infinite number
of 1st order ones. (Formally, FOL framework never insists that
we have to know about ZFC to formalize a different theory.)

Assuming we've formalized a theory G of "geometry", how could we prove
that the 5th "postulate" - as an axiom - is unprovable in G, without
mentioning anything about ZF(C)? In other words, how could we possibly
come up with a specific model of G in which the 5th is false? Thanks.

What's all this about axioms being proveable in a system? I've never
heard of such a system - how does that work?

.

Relevant Pages

  • Re: A question about FOL theories and models
    ... FOL framework never insists that ... we have to know about ZFC to formalize a different theory.) ... Peano arithmetic, and any stronger theory, such as ZFC. ...
    (sci.logic)
  • A question about FOL theories and models
    ... FOL framework never insists that ... we have to know about ZFC to formalize a different theory.) ...
    (sci.logic)
  • Re: Godel proved maths inconsistent not incompleteness theorem
    ... mathematics in light of set theory. ... ZFC, just the first half or so of those books would be okay - covering ... theory you don't see how to formalize. ...
    (sci.logic)
  • Re: (Not quite) Cantors diagonal proof
    ... with much greater precision than would be possible if we were to work ... > all sets is deemed irregular and non-existent, is not ZFC empty? ... Have you ever tried to formalize this line of reasoning? ... If you are talking about an ordinary pencil, ...
    (sci.math)
  • Re: (Not quite) Cantors diagonal proof
    ... >>it has the same number of repeating digits as the diag but every digit is offset. ... In the to formalize mathematics, ... ZFC formal set theory is notable. ...
    (sci.logic)
Quantcast