Re: Implementable Set Theory and Consistency of ZFC

Jesse F. Hughes a écrit :
Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> writes:

Jesse F. Hughes wrote:

Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> writes:

Jesse F. Hughes wrote:

I did not ask about your needs. I asked whether the formula ~Infinity
is also a theorem of (1)-(4), where ~Infinity is the negation of the
axiom of Infinity.
(~Infinity) is _not_ a theorem of (1)-(4), in this article:

http://hdebruijn.soo.dto.tudelft.nl/jaar2007/set_theory.pdf
Why not?
You show that foundation is true in your model. You conclude (1)-(4)
entail foundation.
~Infinity is also true in your model. Why do you not conclude that
(1)-(4) entail ~Infinity?

It is remarkably difficult to get an answer from you sometimes.
Really?
Really.
I simply cannot "prove" anything (constructively) about something I can
not understand (constructively).

As I just indicated, if your argument for (5) is a proof of (5) from
(1)-(4), then my argument for ~Infinity is a proof of ~Infinity from
(1)-(4). They are essentially the same argument.

Your response seems utterly beside the point. You *do* agree that
every set in your model is finite, yes? Then why isn't this a proof
of ~Infinity?

Just for the sake of "explaining" this crank/troll : somehow, he consider that if (X) is "illegal" ("X" is the proposition 1++=(()+*=3, for instance, or "incolor green ideas sleep furiously"), then the system (1)-(4)+(X) is "broken", and all bets are off for deductions in it, even for deductions not including (X)...
.

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