Ok, since I am really killing some time, let me present
an axiomatic theory of countries :-))))))))
Primitive concept: there is a relation R(X,Y,t)
for X and Y that belong to a class called "things
that may be countries" [that I will call C0]
and t is an instant in time
[let�s forget Relativity for a while], that
represents "X recognizes that Y is a country at instant t"
Definition: Recognized(X,t) = { Y | R(X,Y,t) }
[in words, it�s the set of things that X recognizes
as countries in instant t]
Axiom of Existence: Exists t, Exists X,Y such that
R(X,Y,t) and R(Y,X,t)
Axiom of Country Stability: for every t, there is
a non-empty interval [a,b] such that a <= t <= b and
for every x, a <= x <= b, R(X,Y,t) = R(X,Y,x)
Axiom of country creation: if Recognized(X,a) != Recognized(X,b)
and a < b, then there is a finite crescent sequence
t0 = a, t1, ... tn = b, such that
Recognized(X,tn) # Recognized(X,t(n+1))
is an unitary set [for A # B = (A union B) - (A inter B)]
Definition: a function f: [a, b] -> C0 is called a "United Nations"
iff:
(1) f(x) has at least 2 elements, and is finite, for every x
(2) for any X,Z in f(t), there is a chain Y0 = X,
Y1, ... Yn = Z such that R(Yi,Yi+1,t)
(3) for any X in f(t), the set { Y in f(t) | R(Y,X,t) } doesn�t
have less elements than the set { Y in f(t) | not R(Y,X,t) }
Oops. Time killed O:-) I will complete the definition
later...
Alberto Monteiro
