List of first-order-logic notes:

• Free variables
• Logical Axioms and Rules of Inference
• Satisfaction in First-order Logic
• Relationships between models
• Notation for First-order Logic
• Model Theory for First-order Logic
• Consistency and Satisfiability
• Definable elements
• Universal and Existential statements
• Examples of elementarily equivalent models
• Ehrenfeucht-Fraisse Game
• Generated submodel
• Completeness theorems
• Löwenheim-Skolem-Tarski Theorems
• Set of witnesses
• Adding definitions to models
• Peano Arithmetic
• Weaker theories of arithmetic
• Real closed field
• Type in model theory
• Realizing and omitting sets of formulas