Math Forum / Mathematics / Mathematical Logic / November 2005

Hello everyone.  I keep wanting to become "famous", perhaps by proving
something in advanced mathematics.  The reason is that a lot of people
do not understand how severely disabled I can be, even though I am
very smart in some ways, and if I became famous the autism that _I_

consider a language with one relation symbol R and the theory that
claims: there are n elements or more of the domain that are in the
extension of R and there are n elements of the domain or more that are
in the extension of \neg R (negation of R) -- for all n.  this theory

suppose that f is analytic on the disk |z|<=1. Show that there is a
positive integer n such that f(1/n) =/= 1/(n+1).
Need help.

I'm am learning logic from Copi's book (as a hobby). There is an
advanced problem:
With the rules of inference, prove the validity of:
A

I'm stumped by an exercise in Suppes's 'Aximomatic Set Theory' (page
102, Dover). It's a crucial theorem for his treatment, so I am ardent
to have a proof of it.
Here's my formulation of it:

Recently had a email from South-America wanting to know what my
counterexample was for the 4-color mapping since it is a ill-defined
problem. I gave my counterexamples I believe circa 1999, but perhaps I
should re-do that work in a more clear and concise exposition.

Can I say that the degree of achieving a conditional statement (if x
then y) is equivalent to a conditional probability p(y|x)?

I'm newish to logic - background is computer science...
I'm trying to understand the turnstile symbol |-, and its use within
proofs (specifically proof trees). I understand that |- means
'yields' or 'proves', in the sense that it's a statement that

I would like to read some opinions about this:
http://front.math.ucdavis.edu/math.GM/0510469

What do we know about equality?
C-B

i have two questions - would be greateful for any refernces:
1) is there an axiomatization of the theory of rational numbers?
2) is that theory complete?
thank you

i have a question about model theory that i am quite confused about
that i wish someone could please help me with.
i am confused about what notions of infinity are and are not first
order representable. clearly we can have an infinite set of sentences

My vote goes to Gregory Chaitin - hands down.  What say ye?
C-B

On page 84 of Suppes's 'Axiomatic Set Theory' (Dover), he mentions an
"intriguing" exercise (and he says, "the problem is to prove it"). But
the exercise seems trivial to me while there are exercises in the book
that are much harder but with no mention that they are difficult. So I

We can construct a language and semantics for ramified type theory
without extensionality as follows. (This seems to be the semantics that
Bertrand Russell had in mind in Principia Mathematica).
We have the type of individuals. Then if we have already constructed