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Robbins algebras satisfy the axioms of Boolean algebra.

The Claim

Every Robbins algebra is a Boolean algebra.

Verified by Lenz ·

The Short Version

The universal statement is a settled mathematical theorem. McCune’s 1996 automated proof established that associativity, commutativity, and the Robbins axiom imply the axioms of Boolean algebra; subsequent peer-reviewed work verified and clarified the proof rather than overturning it.

Caveats

  • The statement assumes the standard definition of a Robbins algebra: a structure satisfying associativity, commutativity, and the Robbins axiom.
  • Many secondary webpages repeat the same underlying result and should not be counted as independent proofs.
  • The proof was computer-assisted, but later verification and revision supported rather than invalidated it.

The Receipts

  1. Solution of the Robbins Problem | Journal of Automated Reasoning

    link.springer.com

  2. Robbins Algebras Are Boolean: A Revision of McCune's Computer ...

    sciencedirect.com

  3. Computer Math Proof Shows Reasoning Power

    archive.nytimes.com

  4. Boolean Algebra -- from Wolfram MathWorld

    mathworld.wolfram.com

  5. Robbins Conjecture -- from Wolfram MathWorld

    mathworld.wolfram.com

  6. Solution of the Robbins problem. (Journal Article) | OSTI.GOV

    osti.gov

  7. Robbins algebra

    en.wikipedia.org

  8. Robbins Algebras Are Boolean - UNM Computer Science

    cs.unm.edu

  9. Robbins Algebra

    cs.unm.edu

  10. Solution of the Robbins Problem

    cs.unm.edu

+ 9 more sources — see the full list on Lenz

Filed Under

Boolean AlgebraRobbins Algebra