FOM: Two axioms of set theory

[Kazimir Majorinc]

Dear colleagues,


Consider these two axioms for (naive) set theory:

    (1)  Weak Anti-Choice:
         -----------------
         One can not define or choose natural number greater
         than M with set theory axioms (except this two) or 
         without reference to M.

         "Tell me the number and I will tell you that it is smaller than M" 


    (2)  Strong Anti-CH:
         ---------------
         c = aleph_M 

M is new constant (like 0) natural number, described with axiom (1). 

I have two questions for more experienced colleagues:

    (1)  Which are the possible problems and consequences?
    (2)  Are these axioms (as pair) considered before in this or similar form?


Introduction:
=============
Kazimir Majorinc, dipl. ing. math., absolved in philosophy,
theology, anthrophology, professional colaborator at Faculty 
of Natural Sciences and Math., University of Zagreb, Croatia;
Member of Seminar for Fundation of (Mathematics and Computer Science), 
at same university; author of few works in mentioned branches and one 
book in logic. 
 
Sincerely,
   
______________________________________________________________
           Kazimir Majorinc, dipl. ing. math.                 
  Faculty of Natural Sciences and Math, University of Zagreb  
 mailto:kmajor at public.srce.hr   http://public.srce.hr/~kmajor 
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