Mathematical Infinity, Its Inventors, Discoverers, Detractors, Defenders, Masters, Victims, Users, and Spectators.

Edward G. Belaga (1)

1 IRMA - Institut de Recherche Mathématique Avancée

"Is Mathematical Infinity adequately captured by Cantors set theory ? Or, for that matter, by Zermelo-Fraenkel, ZF(C), axiomatic and its modern extensions ? What is the meaning of the foundational crisis of nearly unprecedented magnitude (paraphrasing [Friedman 1986], p. 93) which the higher set theory is going through, almost uninterruptedly, for the last hundred years, and what are the good mathematical lessons one can learn from it ? We address here these and related questions, extensively using in our search widely conflicting, but also immensely rich ideas of many of the leading researchers in set theory and beyond. "

Mots clés: "Set theory; Zermelo-Fraenkel axiomatic; axioms of infinity; transfinite recursion"; Set theory; transfinite recursion

Domaines: Mathématiques générales [math.GM]

Edward G. Belaga. Mathematical Infinity, Its Inventors, Discoverers, Detractors, Defenders, Masters, Victims, Users, and Spectators.. 2000. ⟨hal-00129653⟩