Math Forum / Mathematics / Mathematical Logic / June 2007

Let B={1,2}
Let N={1,2,3,....}
Let C={ f | f:N->B }
What is the proof in ZF that |C|>|N| ?

The following is my last corrected version of my ZFUZ theories
http://zaljohar.tripod.com/index.html#zfuz
Two questions:
Is there any inconsistency with these theories?

How identity is defined exactly?
In second order logic one can use the following axiom to define
identity:
AxAy( x=y <-> AP(P(x)<->P(y)) )

I would like to form a set theory that can surve as the basis for
logically consistent scientific theories. I would like this theory to
have non logical primitive predicates like 'x is a man' ,
'x is a proton' etc.... , I will call this theory 'Sci'.

So, humans basically want to believe that ultimate justice is a bad
thing, they don't like the idea of a world where everyone is innocent.
They want to believe that selfishness and sadism is a "good" thing.
Well, if it was good, it wouldn't be selfish or sadistic. If you were

Can the consistency of the theory of division rings be proved in
Bounded Arithmetic?

Does logic belong to philosophy or mathematics? Who could tell me.

In his "Set Theory", Kunen says that a map f:a->b maps a "cofinally"
into b if range(f) is "unbounded" in b.  What on earth does he mean by
"unbounded" here?  The word is not in his index (nor is "bounded") and
I can't find it anywhere.

The correct definition of Nelson Goodman's famous predicate "grue" has
been the subject of some controversy.  Goodman's original definition
is somewhat difficult to find online because most people do not quote
Goodman verbatim, but instead offer their own paraphrase.  So, I have

i would like to know if the following first-order-logic formulas are o.k.
I am not sure about the use of material implication.
I would be grateful if you help me.
(1)  "Everyone has someone that they love."

So basically, most people live by some form of code. It's far less
these days, but it used to be far more so. We had religions, or
customs, or traditions. We have laws. We have social expectations.
So basically, nasty selfish beings like humans need codes to survive.

Does anyone know what 'a conjunctis ad divisa' means? I found it in a
logical work by Scotus that I am translating.  Google reveals that
Locke uses the same phrase in "Four letters concerning toleration"
http://www.humboldt-studienzentrum ...

I'm getting near to the end of doing a paper-by-paper review of the
Olszewski collection on Church's Thesis after 70 Years on my blog.
Actually, I've found putting my thoughts into enough order for me to
be able sound off there has been a very useful exercise (and promising

Sorry, but I searched the term infinity in the group and found
hundreds and hundreds of results, but after an hour or so of digging,
I couldn't find the answer to this seemingly simple question:
Is (infinity) the same as lim (x) as x --> (infinity) ?

i enjoy grabbing a random book on saturday mornings
 opening to any page
and trying to understand interpretations in my modern reality
it is a telephone game of mapping