Math Forum / Mathematics / Mathematical Logic / December 2004

Does it exist a definable arithmetical formula representing a relation which
is not r.e.?
For example:
can I choose a polinomial P(x,y,z) such that the relation

Let L be a finite list indexed to natural numbers, such that:
(I) Each list member, n, consists of n symbols; (II) For m from
1 to n, the m_th symbol of the n_th list member is a circle with
m dots inside.

Can anyobe explain me what is the difference between a structure and a model?
Thanks,
Ori.

The following construction would seem to establish that V=/=L in
Morse-Kelley set theory. Can anyone point out the stupid mistake I'm
making here?
Let S_phi_i be an enumeration of the Skolem functions for L. Define a

It follows by construction that if X is consistent, then V[M](X) = 1
(ie, there is a valuation V based on a model M of X where X is true)
and for each formula @ e X, V[M](@) = 1 too.
But supposed X is inconsistent, does it then follow that V[M](X) = 0

there are often threads in this group concerning
the cardinality of the set of real numbers. Some
persons seem to have strong objections against the
Cantor Proof of the fact that the set of real

Emergence is the process of deriving some new and coherent structures,
patterns and properties in a complex system. Emergent phenomena occur due to
the pattern of interactions between the elements of a system over time.
Emergent phenomena are often unexpected, nontrivial results ...

I've long maintained that there are no "infinite
sets", and in particular no "infinite set of all X"
where X is any type of cardinal, because, first,
the terms are inherently contradictory ("all"

Until now I had believed the superior strength of the USA democracy was
that it fostered 2 party rivalry and competition and that 3 parties or
more caused weakness in the system. For instance Germany preHitler was
strong 3rd party. That whenever a democracy loses its 2 party rivalry

Can we define truth as 'contains itself'?
very few things do contain themself, an idea, a bucket holder holder, set of all sets.
The abreviated liars paradox
f = ! f

I have observed our democratic system of government for over 30 years
now and have come to some scientific analytical conclusions.
For one I believe all political systems are transitory and moving
towards better and stronger forms of government. That means that

Suddenly I found myself confused when thinking about FOL and Gentzen
systems. I'd appreciate some help getting my thought back on track.
This sequent should be (easily) falsifiable, right?
  |- Exists x . P(x)

I am able to do this now because most of Josephus Antiquities history is
on the Internet. Back in 1990s I could not do this because I would have
had to make a full research and drop my science which I was in no
ambition to do. But now I can do this in full satisfaction.

What Is Thought? By Eric B. Baum, 2004, a book that explains that
humans did not evolve a brain that is meant for logic thinking in
everyday life, rather, it's mostly the cognitive elites that have this
ability, a tiny fraction of the human population.  Here is a very good

Peer review
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