Powerful Words: The ZF Axioms

notes
llm
set theory
The ZF axioms are represented by powerful, political-sounding words…
Author

Stephen J. Mildenhall

Published

2025-08-21

Modified

2025-08-21

union

choice

pairing

infinity

separation

foundation

extension

replacement

The names of the Zermelo-Frankl axioms of set theory are a powerful and evocative set English words—they could be a political manifesto. The ZF axioms are the foundation of modern mathematics.

Words so powerful, they go on a T-shirt.

Words so powerful, they go on a T-shirt.

ZF Politics

  • Union: solidarity, bringing people together across divides; strength in numbers. We stand together, stronger than the forces that would divide us.

  • Choice: individual liberty, autonomy, the right to decide one’s path. Every voice has the right to decide its own future.

  • Pairing: partnership, alliance, friendship, the strength of cooperation. We form alliances, partnerships, and communities of mutual aid.

  • Infinity: boundless possibility, the refusal to be limited by old constraints; hope without end. Our imagination for justice knows no bounds.

  • Separation: liberation from oppression, the courage to part ways with unjust structures. We cut ties with oppression and those who profit from it.

  • Foundation: stability, justice, principles on which a society can endure. We ground ourselves in fairness, truth, and dignity.

  • Extension: growth, inclusivity, reaching further than before. We stretch our hand further, to include the excluded.

  • Replacement: renewal, reform, the courage to change what is broken. When old systems fail, we build new ones in their place.

Fractal-esque infinite union of revolutionaries.

Fractal-esque infinite union of revolutionaries.

The ZF Manifesto

Union in revolution,
Infinity of execution.

Separation from tyranny,
Replacement with sanity.

Choice for every kingdom,
Foundation in freedom.

Pairing strength with solidarity,
Extension to all humanity.