FOM: Axion's objetive

[Franklin Vera Pacheco]

 It hapens that the axiomatic constructions are intended to represent all 
the intuitive characteristics of the theory. eg, We give a union axiom 
because we intuitively always can get the union of whatever two sets.
 It hapens too that because of this there are,in the theory, some 
operations that we can't do. Some times the theory acerts the existence of 
an element that we can't construct or very strong proposition as the 
induction principle. 
 It maybe can be interesting to make an axiomatic construction that is 
intended to represent  the human capability ( finitistic 
thinking,constructions, deductions)

 To see this in a better way:

   1)there are not infinitely many elements
   2)for the naturals we can get the 0,the sucesor axiom but not the 
induction one.
   3)all the infinite sets only can be given as the rule ( finite ) to get 
its elements..



 Does someboddy know some work near this?   

-- 
Franklin Vera Pacheco
45 #10029 e/100 y 104
Marianao, C Habana,
Cuba.
e-mail:franklin at ghost.matcom.uh.cu
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