Abstract
Since Cohen’s discovery of forcing, many problems in set theory have been proved to be independent of ZF-set theory just as in the case of the parallel postulate in plane geometry. In plane geometry, only the independence of the parallel postulate was considered, but in set theory it seems that infinitely many problems can be proved to be mutually independent. The consideration of many set theories might not be of advantage to us because set theory is a basis of mathematics and working mathematicians cannot believe that both “yes” and “no” are equally reasonable answers to their problems in natural numbers, real numbers or Hubert spaces.
Part of this work was supported by NSF GP-4616. The outline of this work was discussed in a symposium on the Current Status of Set Theory at a joint session of ASL and APA held on December 28, 1965.
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Takeuti, G. (1969). The Universe of Set Theory. In: Bulloff, J.J., Holyoke, T.C., Hahn, S.W. (eds) Foundations of Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-86745-3_8
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