Volume 6 — Meta-Logic and Reflexivity
Self-Reference and Incompleteness in Golden-Base Systems
This volume explores the meta-logical properties of φ-constrained systems. Through Gödel coding, fixed points, and self-reference, we discover the inherent limitations and paradoxes that arise when collapse structures attempt to describe themselves.
Chapter Index
Chapter 096: LogicCollapse
Collapse-Coherent Logic beyond Truth Tables
Logic that transcends binary truth through structural coherence.
Chapter 097: GodelTrace
Gödel Coding via φ-Trace Symbol Sequences
Encoding logical statements as trace sequences.
Chapter 098: UndecidableCollapse
Collapse Reachability as Logical Incompleteness
Undecidability emerges from unreachable trace configurations.
Chapter 099: TuringCollapse
Collapse-Turing Equivalence via Trace Machine Encoding
Proving computational equivalence with Turing machines.
Chapter 100: FixpointCollapse
Self-Referential Fixed Points in Collapse Structures
Fixed points where traces reference themselves.
Chapter 101: MetaSystem
Collapse-Aware Meta-Logical Frameworks
Systems that reason about collapse systems.
Chapter 102: CodexSelfModel
Codex as Reflexive Meta-Interpreter of Its Own Structure
The codex understanding itself through its own framework.
Chapter 103: CollapseProof
Structure-Driven Deduction Nets over φ-Trace
Proof systems built on trace transformations.
Chapter 104: DiagonalCollapse
φ-Trace Diagonalization and Collapse Limitation
Diagonal arguments in trace space revealing limits.
Chapter 105: RecursiveCollapse
φ-Recursive Function Construction via Trace Evolution
Building recursive functions through trace iteration.
Chapter 106: ModalLogicCollapse
Modal Layer Logic on Observer-Sensitive Trace Nets
Modal logic with observer-dependent modalities.
Chapter 107: CollapseCategoryLogic
Collapse-Aware Category-Theoretic Semantics
Categorical logic for collapse structures.
Chapter 108: ConsistencySpectrum
Collapse Inconsistency Spectrum and Trace Conflict Detection
Measuring degrees of inconsistency in trace systems.
Chapter 109: CollapseAxioms
Structural Collapse Foundations of Formal Systems
Axiomatizing collapse-based mathematics.
Chapter 110: CollapseIncompleteness
Trace Systems that Cannot Describe Themselves Fully
Incompleteness theorems for collapse structures.
Chapter 111: CollapseEntropyTheorem
Entropy-Bounded Meta-Structure Collapse Limit
Entropy limits on self-description complexity.
Key Concepts Introduced
- Meta-Logic: Logic about collapse logic
- Gödel Encoding: Statements as traces
- Self-Reference: ψ = ψ(ψ) at logical level
- Incompleteness: Inherent limitations
- Fixed Points: Self-referential structures
- Modal Collapse: Observer-dependent truth
Dependencies
- Volume 2: Basic logic foundations
- Volume 5: Spectral analysis for entropy
- Volume 7: Observer systems
Next Steps
- Volume 11: Computational implications
- Volume 15: Category theory extensions
- Volume 27: Epistemological consequences
"To know collapse is to collapse knowing itself."