FOM: Two axioms of set theory

Kazimir Majorinc kmajor at
Fri Jan 16 00:28:19 EST 1998

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?

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. 
           Kazimir Majorinc, dipl. ing. math.                 
  Faculty of Natural Sciences and Math, University of Zagreb  
 mailto:kmajor at 

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