Quillen’s “small object” argument uses a variant of this procedure to construct a factorization of morphisms into two terms. For 10 points each:
[10h] Name this procedure that requires a well-ordered set and the axiom of choice. This procedure involves verifying a “successor case” and a “limit case” to show that a property “P of alpha” is true for all alpha.
ANSWER: transfinite induction [accept transfinite recursion; prompt on induction or recursion]
[10m] Gerhard Gentzen used transfinite induction up to a particular ordinal in his consistency proof for this set of statements. An Italian mathematician names these statements that define the natural numbers.
ANSWER: Peano axioms [or Peano postulates; or Dedekind–Peano axioms; or Dedekind–Peano postulates; accept “Peano’s” in place of “Peano”]
[10e] Transfinite recursion can be used to construct a “universe” of well-founded sets named for this polymath. This Hungarian-born “father of game theory” wrote Mathematical Foundations of Quantum Mechanics.
ANSWER: John von Neumann [or Neumann János]
<Ohio State B, Other Science>