Math Forum / Mathematics / Mathematical Logic / July 2009

Language : FOL with identity
Primitives: =,e
Define: y subset x <-> for all z ( z e y -> z e x )
Axioms:

I am currently echewing on a little hypothesis I am
not sure about. Lets assume we have S4, and now we
add the following axiom schema:
    L(A -> c) v A      (Clavius)

Let D be any class (possibly a set). We wish to know if a given set x
or any of its sets, or any of the sets of its sets, or... contains an
element of D.
It looks like for every set x there must exist some subset S of R(rank

Is written in the subject line of the message directly above this
message posted after this message.
You see if randomness exists there is a chance the first part of the
sentence would be different from the second part of the sentence. But

quoting Daryl mc cullough:
1. By definition of K, for any number n, n is in K if and only if Phi_n
[n] is not provable.
2. Since K is definable by Phi_k, Phi_k[n] is true if and only if n is

What is the easiest way to show that we can go
from a 2-ary modal operator:
    A < B: Implication in some substructural logic
To a 1-ary modal operator:

Proof there is no randomness is contained in the subject line of the
message directly above this message posted after this message.

Kurt Goedel proved that a formal system consisting of classical logic
with Peano axioms is syntactically incomplete. That is
    (EP)(|/- P & |/- ~P)
They tell me that this result generalizes to any system that can do a

I should be grateful if you could help me with the following two
questions. If possible, please provide references.
1) Are Tarski's theorem on undefinability of truth and Godel's first
incompleteness theorem equivalent? I know that Tarksi's theorem on

After reading Ignasi Jané's "The iterative conception of sets from a
cantorian perspective" and "¿De qué trata la teoría de conjuntos?" (I
ignore if there is an english translation of the latter), and about
the notion of maximal extensionality (i. e. that a domain has this

What is a 'crank' and what is a 'troll' in numbers? What quantity to
them exists numerical expression of these? If C is as A^2 + B^2 = C^2
and the 'term' rank holds numeric estate, then it is true 'crank' is a
square root of a leg of a triangle multiplied by rank. Do you see why

Episodic Memory: conscious recollection of past episodes.
Episodic memory shares a core neural network with the simulation of
future episodes, enabling mental time travel into both the past and
the future. The notion that there might be something distinctly human

Hi, I was wondering why they don't include the physical effects our
brain produces to create our world as we know it and sense it to 2d
and 3d equations.

http://www.pbs.org/wgbh/nova/einstein/legacy.html
"What hasn't Einstein's equation touched in our world?
It's difficult to separate the enormous legacy of E = mc2 from
Einstein's legacy as a whole. After all, the equation grew directly

I wonder whether the reader ever considered why people established,
amongst others, the so-called "copyright" laws? As it turns out, a
main reason why copyright laws were introduced, and also why people
practice industrial secrecy, professional confidentiality, secret