Summary
This chapter explains and demonstrates logical independence of the imaginary unit, in relation to the Field Axioms.
Examples of logical independence in Elementary Algebra; and how Soundness and Completeness Theorems, from Model Theory, a branch of Mathematical Logic, are used to show existence of the imaginary unit is logically independent of the Field Axioms.
Other Chapters
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Title & Preface
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Contents
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Index
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The Question of Quantum Indeterminacy
What are the Fundamentals of Quantum Indeterminacy? -
Quantum Mathematics: Logic in Semantic Interpretations
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Elementary Algebra: The Inherent 3-valued Logic Within
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Logical Independence:
Information, neither Provable nor Negateable 
Preview
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The Vienna Experiments:
Logical Independence and Quantum Randomness -
Logical Independence in Applied Mathematics:
The Role of the Imaginary Unit -
Verifying Logical Independence of the Imaginary Unit:
The Soundness & Completeness Theorems -
Pure State Vienna Experiments are Non-Unitary:
Pauli Algebra is not Exactly Isomorphic with Pure States -
Matrix Representation of Indeterminate Information:
Step-Transition between Pauli and Pure State Matrices -
The Inaccessible Lost History at Measurement:
Irreversibility in the Density Operator at Measurement -
Redundancy of the [Hermitian] Unitary Postulate:
Unitarity is an a posteriori implication of complementarity -
Logically Independent Unitarity in the Free Particle:
Internal Self-Reference and Consequent Unitarity -
Logically Independent Unitarity in the Pauli System:
Internal Self-Reference and Consequent Unitarity -
The Revised Approach to Unitarity:
Faithful Isomorphism through Unitary On-Off Switching -
Self Reference: The Origin of Uncausedness:
Spontaneous Creation of Structures Needed for Mixed States -
The Indefiniteness of Indeterminacy: Referential Ambiguity and the Epistemology of Perfect Symmetry
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The Uncausedness of Indeterminacy:
In Quantum World, Cause is not Identical to Non-Prevention -
Concise Statement of Indeterminacy
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Appx: Quantum Self-Reference and the Classical Paradoxes: Cantor's Diagonal and Cantor's Theorem
