Finney's Theorem

Finney's Theorem addresses the stability of logical systems, specifically showing that certain foundational rules in formal logic hold true when expanding those systems. It ensures that adding new statements or rules doesn't inadvertently cause the system to lose consistency or produce contradictions. In essence, it guarantees that logical reasoning remains reliable and sound even as we extend or modify the underlying framework. This theorem provides confidence that our logical structures can grow without sacrificing their integrity, supporting the development of complex, well-founded formal systems.