Hi all

A set is said to be dedekindian iff the non existence of a proper
subset of it that is equinumerous to it implies it is finite.

x is finite iff exists R (R is a well ordering on x and
converse(R) is a well ordering on x).

In symbles:

x is dedekindian <->
[~Ey (y proper subset of x & y equinumerous to x) -> x is finite].

Zuhair

It's well known that ZF and ZFC have the same arithmetical consequences.
Are there any 2nd order arithmetic systems known that have the same
arithmetical consequences as ZFC?

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.
Scott

We are asking a man a few questions. After every response we can
check, whether he told the truth or deliberately lied. Lets say, at
the beginning, the probability, that the man will lie and the
probability the man will tell the truth are the same (0.5). If the man
answers the first question and lies, the probability that he will also
lie when asking a second question is (I guess) already greater than
0.5. But, if the man will answer first five questions frankly, the
probability, that in the reply to sixth question he will also tell the
truth is already much higher than 0.5. But how high is the propability
exactly, and how do you calculate that?
(sorry for english :)