The Semantic Elevation Operator and the Closure of the Undecidable Class under Preservation

Excerpt

arXiv:2609.11326v1 Announce Type: cross Abstract: The undecidability of a program's static semantic properties is governed by Rice's theorem. Self-modifying systems, however, require analysing not whether a property holds now, but whether it is preserved when the system rewrites itself. We formalise this transition through a semantic elevation operator {\Lambda}{\Phi}, which turns the static question "does x satisfy P?" into the dynamic question "is P preserved after x is transformed by {\Phi}?"