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The Universe of Set Theory

In: Foundations of Mathematics

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  • Gaisi Takeuti

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.

Suggested Citation

  • Gaisi Takeuti, 1969. "The Universe of Set Theory," Springer Books, in: Jack J. Bulloff & Thomas C. Holyoke & Samuel W. Hahn (ed.), Foundations of Mathematics, pages 74-128, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-86745-3_8
    DOI: 10.1007/978-3-642-86745-3_8
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