Math Forum / Mathematics / Mathematical Logic / August 2007

Am I getting confused?
I seem to have lost grips with the nessitation rule
Does it only apply to Theorems/ axioms (valid in all worlds)  or also
to premmisses (valid in some worlds)?

So, you humans, or homo-mendax as is your proper nomenclature, have
created a reality which is totally backwards.
Backwards, you morons. Don't you get it, it's BACKWARDS. You are doing
it backwards.

Hi: Given any set S with transfinite cardinality x, what is the
correct notation for showing a list of this set. For example (using
latex notation):
S = { s_0, s_1, s_2, ..., s_{w_x} }

Does proof  by contradiction require a prior assumption of
consistency ? This is a view which seems to have been put forth in an
article in Mathpages ( http://www.mathpages.com/home/kmath347/kmath347.htm
).

I was studying "the logic of provability" from G. Boolos
And was noticing that he always talks about a finite model of GL.
But after some puzzling i came to the conclusion that GL must be
infinite otherwise if you add the consistency theorem ~P(f) it becomes

The context here is Z set theory.
Let ' * ' stand for cardinal multiplication.
Let ' w ' stand for the set of natural numbers.
We know that ZC (Z plus the axiom of choice) proves

Does logic reasoning need quantifier?
As we know the logic could be divided two parts those are logic
reasoning and logic linguistics. Now we are going to discuss the
question is "does the logic reasoning need the quantifier?". For

I have run into a dilemma defining the Cartesian product. I would
appreciate it if someone could help me out.
1. I define the Cartesian product of AxB as
     AxB = { (a,b) | a in A  <and> b in B }

We can understand some fallacies intuitively, but how can they be
formally proved to be incorrect?
E.g. If we have two premisses:
P1: x is tall

In typical computer languages (imperative, declaritive...C++, SQL,
etc) the processing of AND/OR expressions is done with 'AND' having
precedence over 'OR'.  Is this precedence rule unique to software
computation, or does theoretical and / or general applied mathematics

SRT , GRT and “ Minkowski space “.
SRT doesn't have a gravity field.
If there is no gravity field , the space will be flat,
and this space is called “ Minkowski space “

An axiom to settle the continuum hypothesis ?
Paul Cohen used a set of generic reals to prove the consistency of
the
negation of the continuum hypothesis with other axioms.

Hi, I am new to this group and would like some recommendations on some
good introductory textbooks on non-classical logic, in particular the
algebraic aspect of these logics.  I have already had some exposure to
college level classical propositional and predicate calculus.

My prediction for you, today, and forever, is:
Death, misery, pain and destruction. You will fall away and only live
lives so insignificant before the lives of those of us who are pure
good.

A grandparent is a parent of ones parent
We have conflicting translations into FOL, would be great if someone
could help me clear this up, thanks!
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