[FOM] Naming Infinity / Loren Graham -Jean-.Michel .Kantor

[jean-michel kantor]

  In the early years of the twentieth century, following the creation by  Georg
  Cantor of  set theory, mathematicians were concerned with the
  possibility of developing transfinite numbers.   In France, the leaders were
  Émile Borel, Henri Lebesgue, and René Baire.  They did fundamental work that
  secured their places in the history of mathematics but ultimately they
  hesitated.
  How could they show that the different kinds of infinities that
  they were postulating actually exist?
    Were these new infinities just  groundless speculations?
Russian mathematicians -- especially Dmitri Egorov and Nikolai Luzin --
who came to Paris to study with the French leaders in the field-
were under the influence of a particular religious heresy called Name
  Worshipping whose followers held that they could show  that God exists by
  “naming Him.”  They believed that “the name of God is God.”
  In a similar sense, the Russians thought that they could show that
  the new infinities existed by naming them.  This view fit well with Henri
  Lebesgue’s 1904 introduction of the concept of “naming a set” (nommer un
ensemble).
Following this approach the Russians named many sets of the new
type and developed a new field:  descriptive set theory.
Our book is published by Harvard University Press and gives teh whole story.
See
http://www.cems.uvm.edu/~cooke/infinity.pdf