Math Forum / Mathematics / Mathematical Logic / August 2008

Starting with the smallest infinite ordinal omega, we can look for
points where there's
a jump in complexity.  Omega + 1  is a a successor ordinal; so it's
ordinary.  Same

The laws of bivalence, excluded middle, and non-contradiction are alike
in that as "laws" they act upon objects.
We can say, in that case, that an application of these laws introduces
objects where objects would otherwise have not been up for consideration.

Principle of included middle, is the natural law by which triple is
produced out of couple.-Aiya-Oba (Poet/Philosopher).
  Thus, 2n +  (n + n/2) ...  =  3n
Where n, can be any natural number

For a long time, since the late 30s I guess, the idea of computability
has been more or less definite, standard, agreed, incontestable.
This is the essential content of Church's thesis.
Basic computability extends easily and standardly to

I am having a problem with searching for posts written by Torkel
Franzen using Google Groups. Each search only gives one hit, this
despite the fact that he has written a large number of messages. Does
anyone know why this is the case? Is there another reasonably good way

What logical conclusions will be drawn from “Set A belongs to Set B”
and “Set C belongs to Set D” ?
When this condition inputs to the concept calculator, the following
concept equation was established.

Why do we discard L when
L = L is not true
but we accept G when
G = G has no proof  ?

When this condition inputs to the concept calculator, the following
concept equation was established.
X  /  (Set A < Set B)  *  (Set C < Set D)  =  Dao
This concept equation was solved on the concept calculator and got a

Hi: In order to apply Godel's incompleteness theorem, we need "a
certain amount of arithmetic" in the formal system, which can be
loosely translated to natural numbers and a couple of basic rules
about addition and multiplication. Does anyone know of undecidable

Is it possible to define the following property in the language of
first order arithmetic(S,.,+,0,<):
"for all x<y there are only finite many numbers z such that x<z<y"
If it is, then it should be unprovable in Peano arithmetic(because of

Actually one can define subcardinalities like w-1, w-2 ,..., w/2 , nth
root of w, etc....
Although a lot say that this is not the traditional approach and doubt
it but it can be done.

Is it possible, in ZF (or related theories), to define a function
B(X,Y) such that (1) if X=Ø (the empty set) then B(X,Y)=Y, and if (2)
X is different from Ø (the empty set) then B(X,Y)=P{W:EZ(Z element of
X AND W element of B(Z,Y))}? Here "P" is for the power-set operation.

n*e=o
Hence...
n=o/e
Let n=1, e=0

If you could write a function that identified if a piece of code
contained a reference to the halt function, or analagous code
to the halt function, then you could program a 3 valued halt
function.

When you consider computable reals 0<=cr<1
what variety do you get in the decimal expansions?
Every possible sequence of digits to infinite length
is represented as a computable number.  You might