Question
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>
Summary
| Lower Mid-Atlantic | 2025-02-01 | Y | 6 | 6.67 | 33% | 33% | 0% |
| Midwest | 2025-02-01 | Y | 6 | 13.33 | 67% | 50% | 17% |
| Northeast | 2025-02-01 | Y | 4 | 17.50 | 50% | 75% | 50% |
| Overflow | 2025-02-01 | Y | 4 | 15.00 | 75% | 75% | 0% |
| Pacific Northwest | 2025-02-01 | Y | 2 | 15.00 | 50% | 100% | 0% |
| UK | 2025-02-01 | Y | 10 | 14.00 | 70% | 60% | 10% |
| Upper Mid-Atlantic | 2025-02-01 | Y | 8 | 12.50 | 50% | 75% | 0% |
Data
| Liberty C | Duke | 0 | 0 | 0 | 0 |
| Liberty A | UNC C | 0 | 10 | 0 | 10 |
| UNC D | Liberty B | 0 | 0 | 0 | 0 |
| Virginia A | UNC B | 0 | 10 | 10 | 20 |
| Virginia Tech A | Wake Forest | 0 | 0 | 10 | 10 |
| South Carolina | William & Mary | 0 | 0 | 0 | 0 |