Math Forum / Mathematics / Mathematical Logic / April 2006

I posted this to sci.math but got only one response, which did not seem
to be related to the particular kind of undecidability shown by
Goedel's statement.
About three months ago, I posted, "How can the meaning of Goedel's

In a handbook of mathematical logic I had been found that (if I not
remember wrong):
1º (Compactnes theorem, Gödel Malcev) : Let T be a set of first
oreder logical senteces. If for every

The Real Bible Code really exists, No comments about the famous
versions.
The BOOK FORMAT, created by the AUTHOR is established.
The found out Facts have no any alternative LOGICAL explanation.

Tarski's undefinability of truth theorem proves that we can't define
truth within mathematics because it is impossible to construct the set
of all truths.  But we can still construct a set of all the truths in
mathematics using a meta-system.  What is so amazing about this is you

See discussion started in
http://www.physorg.com/news6713.html
Pentcho Valev

[I posted this to alt.philosophy the other day, but I didn't get a
satisfactory answer there, so I'm trying here.]
An antivirus software vendor tells you that if you don't buy their product,
you will get a computer virus.  Are they using an Appeal to Fear or a

Hello Logic Geeks,
I have a question:
Can the sentence 'Eab & ~Eba' be true on an interpretation for which
the UD contains exactly one member? Please explain.

Does anyone know of any  Pi_0^2  or  Sigma_0^2  sentences that are
known to be undecidable by PA; (and are not reducible to Pi/Si_0^1)?
      _,,--,,_
    /`       .`\

OK, I give up. As Tarski defined it in 1924, "A set is finite if, and
only if, every nonempty family of its subsets has a minimal element,"
where a  minimal element  is a set  not  containing any member of the
family. Could anyone give an (infinite) counterexample?

Have you guys noticed how exhaustive it is to get the most relevent
PLC, pneu/hydraulics information and references, have I. I hence forth
suggest we all work together to make this problem extinct.

...It's an election hall of idiots, for idiots, and by idiots, and it
works marvelously. This is the true nature of democracy and of all
distributed governance. At the close of the curtain, by the choice of
the citizens, the swarm takes the queen and thunders off in the

Hello -:)
This link leads to 4 lambda expressions:
http://www.geocities.com/sebzimm/lambdaEN.jpg
Can someone tell me, how these formulas are gradually derived?

Suppose someone has paranoid delusions. She thinks that everyone is
plotting against her and trying to cause her harm. You try to explain
to her that this conviction is ruining her life, and urge her to get
some treatment. But of course she just thinks you are saying this for

What is the size of the set of all distinguishable infinities? That's a
nonsense question according to mathematicians, but given that they do
not believe in a system of math that is based on correspondence, but
rather that of coherence, how can they debunk a parallel system of

Definition
==========
Let's define rPA, the 1st order "Relativistic Peano Arithmetic" formal
system, in the following manner: