Re: continuum hypothesis and 0=1

On Mar 16, 7:41 pm, Aatu Koskensilta <aatu.koskensi...@xxxxxxxxx>
wrote:
On 2007-03-16, MoeBlee wrote:
Isn't there something about some kind of equi-consistency of ZF and
PM?

Nope. ZF(C) is much stronger than the simple theory of types.

Or is it equi-consistency of Z and PM I heard about?

Probably.


I thought that Z proved the soundness of PM. You can define a truth
predicate for the language of PM in the language of Z, and then prove
that PM is sound in Z by induction on the number of the highest type
that occurs in a sentence.

--
Aatu Koskensilta (aatu.koskensi...@xxxxxxxxx)

"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus


.

Relevant Pages

  • Re: Godel proved maths inconsistent not incompleteness theorem
    ... The statement "for all sentences P in the language of S, ... are stronger properties that are expressible, ... of theories implied by soundness. ... original comment to be about correctness properties stronger than ...
    (sci.logic)
  • Re: Godel proved maths inconsistent not incompleteness theorem
    ... The statement "for all sentences P in the language of S, ... are stronger properties that are expressible, ... 1-consistency, certainly, e.g. soundness for Pi-17 sentences. ... original comment to be about correctness properties stronger than ...
    (sci.logic)
  • Re: interesting study on practicing
    ... learning process than I had considered. ... the stronger the effiency; ... Has anyone here worked through the language courses ... he spoke fluent French after a couple of weeks ...
    (rec.music.makers.guitar.jazz)
  • Re: multimethod + multiple inheritance
    ... Very hard since it influence strongly the efficiency and the design of the language itself. ... What about very large scale programs written in dynamically typed languages (see article "Haskell vs. Erlang, ... C++ has a type system stronger than C and Haskell is strongly typed. ...
    (comp.object)
  • Re: Attn Brian Lafferty
    ... Straight up. ... You're a wuss. ... I'd use stronger ... language to your face but after all this is the internet and this is in ...
    (rec.bicycles.racing)