713 Logic

• Problems Of Philosophy
• Languages And Terms
• L-formula
• L- Sentences
• L-Structures
• Interpretations Of L Terms
• Defining Truth
• Check Definition Of Truth Makes Sense
• Better Notation For Truth
• Defineable And Logical Consequence
• Theory's And Logical Consequence
• Valid And Satisfiable Formula
• Deduction System
• First Order Tautologies
• Substitution
• Defining Logical Axioms
• Generalization Theorem
• Concatenation And Deduction Theorem
• Bound Variable Substitution And Contraposition
• Consistency, Absurdity, and Equality
• Generalization On Constants
• Gödels Completeness
• Completeness Continued
• Completeness Continued Continued
• Completeness Corollary And Compactness
• Listable Subsets
• Complete Sets Of Sentences
• Theories
• Finite Structures And Decideability
• AE Sentences
• Recursive Functions
• Recursive Relations
• Sequence Operations
• Godels Beta Function
• Strict Recursion Is Recursion
• Sequence Operations Recursively
• Recursive Proofs
• Robinsions Q And Peano Axioms
• Sigma Formulas And Robinsons Q
• Sigma Formulas And Robinsons Q Continued
• Bounded For all And Robinsons Q
• Representation In Theory
• Recursion And Representation
• Recursion And Representation Continued
• Gödels First Incompleteness
• Church's Theorem
• Boring Undecidability
• Essential Undecidability
• Strongly Undecidable
• Rubric For Reductions
• Unnested Formula
• Expansion By Definition
• Moving Decidability Via Expansion Lemmas
• Moving Decidability Via Expansion Of Definitions
• Moving Decidability To Sub structures
• Examples Of Transfers
• Interpretations
• Examples Of Interpretations
• Transfer Decidability Via Interpretation Setup
• Transferring Decidability Via Interpretation
• Weirdness Of Complex Numbers
• Decidability Of A Binary Relation
• Recursively Enumerable
• Weak Representation
• Equivalence Of Recursively Enumerable And Weak Representation
• Corollaries To The Equivalence
• Diophantine Subsets
• Sketch Of Recursively Enumerable Implies Diophantine
• Corollaries To Diophantine Iff Recursively Enumerable
• Exposition For Gödels Second Incompleteness
• Proveability Predicates
• Models Of Not Con(PA)
• ZFC Strictly Stronger Than PA (trivially)
• Goldstein Sequences
• Classes Of Functions
• Partial Recursive Functions
• Graph Of Partially Recursive Functions Are Recursively Enumerable
• Recursively Enumerable Equivalences
• Universal Partial Recursive Functions
• Parameter Theorem
• Halting Set
• Recursion Theorem
• Many One Reducibility
• Complete r.e. Sets
• Oracle Partial Recursive
• Turing Reducible
• B Recursively Enumerable And Jump Sets
• Pi1 Formulas
• Hierarchy Of Sigma/Pi Formulas
• Analyzing Arithmetic Sets