Math Forum / Mathematics / Mathematical Logic / December 2005

Can anyone here help me to solve one task from my study. I tried to
find a solution for it by myself but hanged up.
I have a logic function F(A,B,C). After a simplification I received a
simple function as following:

Given a setting of natural deduction.
natural negation (two equivalent systems)
(1)    add logical constant f
    define ~p as p -> f

I'm currently working through Suppes' Axiomatic Set Theory, trying to
fill in gaps in my knowledge. I begin reading, and realize this book
mixes together logic and set theory. I then said, well maybe I should
learn formal logic, too. So I begin reading on the web and see

Sorry, it is a Goedel again.
I just wondered if any of you cognoscenti would be so kind as to cast a
quick glance at
http://www.columbia.edu/~hg17/Diagonal-Cantor-Goedel-05.pdf

is it possible to have a language that can express theories that are
not 1st order representable--meaning there's no 1st order logic theory
such that it has exactly the same models as the theory--and still have
the language be decidable?

Peano axioms

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In mathematics, the Peano axioms (or Peano postulates) are a set of

[I'm crossposting this message to sci.logic and it.scienza.matematica]
(Subsets and predicativism)
When we have built a house, we have already built every its part, so we can
consider as given every its part.

What does 1+1=2 really mean?
Is the equation 1+1=2 a theoretical equation in which the equal sign is
like an ultra sensitive balance scale that requires all parameters of
different items to be identical at all times in order for the balance

Defining, "the word" that  was made flesh  ?
Every Christmas we celebrate the birth of Jesus Christ, a Jew, born of
into a Jewish family, who was suppose to be 'the messiah'...but was he
?  This was suppose to be 'the word' made flesh...?  Was he ?  What

[I'm crossposting this message to sci.logic and it.scienza.matematica]
I call "falsifiable" a sentence S of PA such that a proof of not-S can
consist of a finite numerical verification.
For example, Goldbach Conjecture is falsifiable, whereas Goodstein's theorem

It is possible to prove in ZF+AD that Lebesgue measure is countably
additive?

I am looking for the formal name of the logical fallacy in which a
person distorts or denies evidence in order to retain a foregone
conclusion.  The principle is, I think, related to the ideas of
prejudice or preconception.

Godel's Incompleteness work depends heavily on the assumption
that the theory T in question be consistent. But how could we know
if T is consistent, for any given general T? It seems like we don't
have a precision procedure to determine that. So Godel's results

Folklore has it that it was Kreisel who first noted that the
requirement of omega-consistency in the statement of the second half of
Gödel's First Theorem can be weakened to 1-consistency. Anyone happen
to know when and where?

Protagoras was the author of the famous saying, "Man is the measure of
all things; of what is, that it is; of what is not, that it is not."
This saying puts in a nutshell the whole teaching of Protagoras.
Indeed, it contains the essence of the entire thought of the sophists.