Math Forum / Mathematics / Mathematical Logic / January 2007

In Gentzen's wonderfully lucid and accessible lecture "The concept of
infinity in mathematics" there is an interesting -- and from a modern
perspective -- somewhat puzzling slide. He urges on us a hierarchical
picture of the universe of sets, where "new sets may be formed only

Could anyone kindly point me to a nice treatment of (infinite)
ordinals from a category-theoretic stance? (Axioms for the category of
ordinals, anyone?)
I'm lucky enough to have access to a world-class maths library, so it

It's well known that Tarski's Axiom implies both the axiom of choice
as well the existence of inaccessible cardinal numbers. Does anyone
know other interesting results TA implies, and what other interesting
results can be obtained in Tarski-Grothendieck set theory? (As opposed

I'd be grateful for suggestions for some class-room examples of
relatively easy-to-understand cases where nice, natural, mathematical
proofs proceed by transfinite induction over small ordinals like \omega
+1 or \omega +\omega or perhaps \omega^{\omega} etc.

riplin@Azonic.co.nz wrote:

I have the impression that only the fiercest zombies are still
defending Einstein's idiocies. Other members of Einstein's criminal
cult are mercilessly removing Einstein's name from their websites while
looking for another money-spinner. Bad news comes from everywhere:

http://www.bnl.gov/community/Tours/EinsteinPics/Einsteine.jpg
See also
http://www.bnl.gov/community/Tours/TYSaDTW.asp
"Einstein! Einstein!....The lecture was followed by a rousing game of

I'm a cannibal and I must admit that American women are very edible
and incredibly yummy and it's time to cook and eat as many of them as
possible. Yummy ! Tasty !
Should I roast them on a spit, bake them in a oven, boil them in a

Hypothesis:
Proofs by contradiction are proofs by circularity. Or rather, we might
say that what is presented to a proof is called 'proved' if it is
found as an element or proposition within the circularity of a proof

dear mathematicians and logicians,
is there some way to work out the probability of achieving immortality
in our life-times given that governments have ignored repeated attempts
to advise them in the past several years?

ELECTROSTATICS. The electrostatic theory is based on the assumption
that forces involved in energy changes are CONSERVATIVE. The following
quotation makes the assumption clearer: "We must remember that the only
physical fact underlying this discussion is Coulomb's law, the

I want to prove
~Aa ~Ab R(a,b)  ->  Ab ~Aa ~R(a,b)
without making use of existential quantifiers.
Any help would be appreciated.

If a theorem asserts that something is true, then I understand the
logic of proof by contradiction.
Theorem:  Q is true.
Proof:  Assume ~Q true.

Is there an entropy associated with all the various ways to group elements
into sets? Thanks.

I have been posed a question I should be able to answer. I am actually
not so.
The metatheory of propositional calculus (PrC) contains three results
that seem inconsistent.