Why sets?

  • Authors:
  • Andreas Blass;Yuri Gurevich

  • Affiliations:
  • Mathematics Department, University of Michigan, Ann Arbor, MI;Microsoft Research, Redmond, WA

  • Venue:
  • Pillars of computer science
  • Year:
  • 2008

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Abstract

Sets play a key role in foundations of mathematics. Why? To what extent is it an accident of history? Imagine that you have a chance to talk to mathematicians from a far-away planet. Would their mathematics be set-based? What are the alternatives to the set-theoretic foundation of mathematics? Besides, set theory seems to play a significant role in computer science; is there a good justification for that? We discuss these and some related issues.