|
|
Daryl McCullough wrote:
Aatu Koskensilta says...
And of course, from the observation that ZFC* is acceptable on basis of
our picture of the world of sets, we see that ZFC** with a second truth
predicate covering also formulas involving the truth predicate of ZFC*
is also acceptable, and similarly for ZFC*** and so forth.
How do this sequence of theories fit in with Morse-Kelly set theory?
I'm pretty sure that ZFC* is still a subtheory of MK, but I'm not
sure about ZFC**.
All the theories ZFC*, ZFC**, ZFC*** and so forth, and the theory with
autonomously iterated hierarchy of predicative proper classes I outlined
are interpretable in MK in a natural fashion. MK is much stronger than
any of these theories, and proves in particular their soundness for
sentences in the language of set theory.
--
Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)
"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
|
|