Rigidity is undecidable
Miko{\l}aj Bojanczyk, Stanis{\l}aw Szawiel, Marek Zawadowski
TL;DR
This paper proves that determining whether a finite set of regular-linear axioms defines a rigid theory is an undecidable problem, highlighting fundamental limits in formal logic and automated reasoning.
Contribution
It establishes the undecidability of rigidity in theories defined by finite regular-linear axioms, a previously unresolved question.
Findings
Rigidity determination is undecidable for finite regular-linear axioms.
The result impacts automated reasoning and formal logic.
Undecidability holds generally for this class of theories.
Abstract
We show that the problem `whether a finite set of regular-linear axioms defines a rigid theory' is undecidable.
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