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Topic: The axioms for ultrafinitist number theory?
Replies: 56   Last Post: Mar 30, 2014 10:20 AM

 Messages: [ Previous | Next ]
 LudovicoVan Posts: 4,165 From: London Registered: 2/8/08
Re: The axioms for ultrafinitist number theory?
Posted: Mar 23, 2014 3:20 AM

"Dan Christensen" <Dan_Christensen@sympatico.ca> wrote in message
> On Sunday, March 23, 2014 2:24:05 AM UTC-4, Julio Di Egidio wrote:
>> "Dan Christensen" <Dan_Christensen@sympatico.ca> wrote in message
>>

>> > Axioms rewritten with binary predicate S for the successor relation and
>> > set membership 'e' for epsilon:

>>
>> You have changed nothing of substance,

>
> True. They are cosmetic changes: S(x,y) instead of (x,y) in S.
>

>> and your induction schema is still crippled.
>
> I think you will find that it works.

Idiot. I have given you a counter-argument that you have just ignored.
Here it is again:

Take your proof that all elements but zero have a predecessor (*) then try
the same proof with the added axiom that max has no predecessor: the proof
goes through just as well! I.e. your induction axiom is crippled, and your
system does not capture only finite models. And this was already explained

(*) <http://dcproof.com/ExistenceOfPredecessorsFinite.htm>

>> > It can be formally proven (374 lines in DC Proof format) that these
>> > axioms
>> > are satisfied by:

>>
>> > n = {0, max}, max=/=0 and S(x,y) <=> x=0 & y=max
>>
>> It can also be proved that omega_0+1 is a model for your axioms.

>
> Not sure what that means.

It means your axioms are not only satisfied by finite models. Or you just
don't know what omega_0+1 is?

BTW, I'll take the chance, before I finally killfile you for good, to tell
you something: Do you really think that being a patent liar and a obnoxious
moron, and the insults to e.g. WM just because you feel strong that other
morons stand on your side, are going to benefit your self-promotion and that
of your petty program? And, talking of that DC Proof, you may be a decent
programmer assuming you did that yourself, but be reassured that you just
suck at reasoning in general and at logic in particular: in fact, you do
not even know what logic is, you think it's a calculus...

And now get lost, you have annoyed me one too many times and you'll never
learn anyway.

Julio

Date Subject Author
3/18/14 Dan Christensen
3/18/14 William Elliot
3/18/14 Dan Christensen
3/18/14 LudovicoVan
3/18/14 LudovicoVan
3/18/14 LudovicoVan
3/18/14 LudovicoVan
3/18/14 Dan Christensen
3/18/14 LudovicoVan
3/18/14 LudovicoVan
3/18/14 Dan Christensen
3/18/14 LudovicoVan
3/18/14 Dan Christensen
3/18/14 LudovicoVan
3/18/14 Dan Christensen
3/18/14 LudovicoVan
3/20/14 LudovicoVan
3/20/14 Dan Christensen
3/20/14 LudovicoVan
3/19/14 Wizard-Of-Oz
3/19/14 Dan Christensen
3/20/14 Wizard-Of-Oz
3/20/14 Dan Christensen
3/20/14 Shmuel (Seymour J.) Metz
3/20/14 Virgil
3/20/14 Shmuel (Seymour J.) Metz
3/20/14 William Elliot
3/20/14 Dan Christensen
3/20/14 William Elliot
3/20/14 Dan Christensen
3/20/14 Dan Christensen
3/20/14 Dan Christensen
3/20/14 William Elliot
3/20/14 Dan Christensen
3/21/14 LudovicoVan
3/21/14 William Elliot
3/21/14 LudovicoVan
3/22/14 LudovicoVan
3/25/14 ross.finlayson@gmail.com
3/22/14 William Elliot
3/22/14 William Elliot
3/22/14 LudovicoVan
3/22/14 Dan Christensen
3/23/14 Dan Christensen
3/23/14 LudovicoVan
3/23/14 Dan Christensen
3/23/14 LudovicoVan
3/23/14 Dan Christensen
3/23/14 Virgil
3/23/14 David Hartley
3/23/14 Dan Christensen
3/23/14 Dan Christensen
3/23/14 Dan Christensen
3/25/14 William Elliot
3/26/14 Dan Christensen
3/30/14 Dan Christensen
3/30/14 Dan Christensen