🚀 go-pugleaf

 Thank you very much for your e-mail.

 The axioms of my (finite models) are precisely the set-theoretical
 atomic statements which express the elementhood relations  between
 the sets (which are given explicitly). 

 As I mentioned, the set-theoretical Models that I exhibited are models
for extremely , extremely meager, weak, anemic, very anemic set-theories.
 Nevertheless they explain clearly the usual misunderstanding  in con-
nection with the  so called Low-Skolem paradox, which is not a paradox.
  
  One can give explicitly tables for countable models  which 
satisfy many of ZF axioms.  For the entire ZF - I have proposed a 
countable model where sets are symbolized by any set-theoretical
formula which starts with the "THERE EXISTS" symbol and which is 
derivable in  ZF.
 In other words, I make a set from any formula which is derivable from
ZF axioms and which asserts the Existence of a set , i.e, a derivable
from  ZF  axioms formal formula starting with an  "Existential Quantifier".
 
 Since there are a countable number of this kind of formulas (since
ZF has countably many axioms) so this model is countable and satisfies
all the axioms of  ZF.   HOWEVER NOTATIONS GET VERY, VERY MESSY  and
they eclipse with dark clouds the crux of the matter.  I love my
meager, anemic  finite set-theoretical models.  Nevermind that they
do not satisfy all the axioms of  ZF !  But they do not kill the
spirit - in fact the spirit glows in them !!

   With best and warmest regards,

                                          Alexander ABIAN

-- 
   The tendency of maintaining the status-quo, Reaction to provocation and
                The tendency of maintaining again a status-quo.  
    TIME HAS INERTIA  and some energy is lost to move Time forward  
  E = mcc  (Einstein)    must be replaced by    E = m(0) exp(-At) (Abian)