Math Forum / Mathematics / Mathematical Logic / May 2008

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         I am reading peasno's axioms. I understand they only include
natural numbers.
What is the first order theory that includes rational numbers.
My questions are as follows -

We will utilize the following three definitions.
Definition 1: A sentence is meaningful if and only if it is a picture
of a possible state of affairs.
Definition 2: A sentence is true if and only if it corresponds to an

Think I have solved the S3 riddle
the riddle is in Modal logic S3 is
"
[][](p -> p) v <><>q is a theorem

Yes, what is the difference between a mapping and a relationship?
Are there any other types of association?

How does logic organize its elements? We note, do we not, the following:
Elements or variables are given two types of "special power": either a
power that brings them together or a power that keeps them apart. There
are no logically expressible elements that have no powers. ...

Occam's razor can be presented as a heuristic maxim: do not use more
than you need. It may be that it can be usefully complemented: do not
discard more than you have to. For an example consider how division by
zero has always been treated. If it is allowed it leads to

If the following axiom is added to ZF, would the resulting theory be
equivalent to ZFC?
Axiom:
for all x , for all y ((x is dedekindian and y subset of x)

A room with a view is a room with a view, whether or not there is a viewer.
Then let's be bold. Objects are made real, ontologically and logically,
by a view. This isn't the quaint idea of a quantum world collapsing into
physical form by a view, nor is it psychologism where an ...

Hi: In my readings on set theory foundations, I haven't run across
mention of whether the set of natural numbers is even (w % 2 = 0) or
odd (w % 2 = 1). Does anyone have information on this topic?
Thanks.

I suppose the primitive recursive functions are supposed
to be those functions that provably terminate, is that right?
But there are functions that are not primitive recursive
that provably terminate.

The australian philospher colin leslie dean points out  the separatio
axiom is impredicative -
zermelo introduced it  to outlaw the
russell paradox which showed naive set theory to be inconsistent- thu

On 26 Mai, 13:23, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote:

If mortality is a necessary property of being human then "All men are
mortal" means what it says.
But if mortality is not a necessary property of being human then we can
allow an "exception to the rule", or the "unique". For example, we can

Using first order predicate logic, how can you prove the invalidity of
this line of reasoning:
All P are Q
Some R are not P