Suppose a reservoir rejects and decides every extension . Only finitely many of those one-point extensions can have accepting tails. If infinitely many did, collect their new points into ; every infinite subset of begins with an accepting successor, so would lie in the family. That would make accept , contradicting rejection. This finite-obstruction fact lets a second fusion preserve rejection of every finite stem.

Ancestors (10)

  1. Acceptance and rejection of finite stems
  2. Fusion proof for open Ellentuck sets
  3. Completely Ramsey set
  4. Ramsey set of infinite subsets
  5. Space of infinite subsets of the natural numbers
  6. Ramsey theory
  7. Combinatorics
  8. Area of mathematics
  9. Mathematics
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