Math Forum / Mathematics / Mathematical Logic / January 2006

Someone please show me the error(s) in the following proof outline:
(1) Following Goedel, in Intuitionistic PA we can define the predicate
IPR(s) which is true iff s is the Godel number of a formula which has
some proof in Intuitionistic PA.

A professor walked into class on Monday and stated, "We
will have a suprise exam sometime this week. On the morning
of the exam you will not know that the exam will be that day."
A logic student reasoned with himself like this: "We can't have

Making use of advice from readers at sci.math, here is my formal proof of
0<1 for an ordered fields. Thanks to all who replied
http://www.dcproof.com/0lessthan1.html
This was generated using my DC Proof software, a PC-based proof

Since I recently proved the 4 Color Mapping in one paragraph relying on
the nonexistence of 5 adjacent countries, made me realize that the same
mechanism of proving 4 Color Mapping is within the Kepler Packing
Problem. So I must review and revise my Kepler Packing proof.

The Vanishing Prisoner - This first account is an excellent case in
point because it defies any rational explanation for one simple reason:
it occurred in full view of witnesses. The year was 1815 and the

In the area of set theory, 'ZF' stands for Zermelo-Fraenkel...
1) but what does the 'C' standard for, in 'ZFC' which I see quite
often?
also, 'CH' stands for Continuum Hypothesis...

MoeBlee writes:

Find a counterexample to disprove

psi(x)).
Does the following example work?

The Compactness Theorem says that,
A set of wffs is satisfatiable iff every finite subset is satisfiable,
or equivalently,
If S |= p then there is a finite S_0 subset S such that S_0 |= p.

For years now I have on and off wondered whether there is a single word
that encompasses the concept of "write him/her off". When we no longer
care about a person and who upsets us too much. So we no longer want to
see them, hear them, or have anything to do with them. So we say ...

Kunen states in his An Introduction to Independence Proofs that it's not
known whether one can prove in ZF that there is a cardinal with
cofinality > omega. Is this still so? What sort of things follow from
the assumption that cf(kappa) <= omega for all kappa? (Not assuming

R is reflexive if  xRx is a tautology.  what do we call R if xRx is a
contradiction?  antireflexive?
R is idempotent if xRx is equivalent to x.  what do we call it if it is
equivalent to not-x?  idemimpotent?

In Enderson's book(second edition), section 2.4, subsection
Tautologies.
In the third remark, the author says
forall x Px logically implies Pc

Suppose x does not occur free in Q. Show that

I do really have no idea about how to prove this.