- 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
- LĂ¶wenheim-Skolem-Tarski Theorems
- Set of witnesses
- Adding definitions to models
- Peano Arithmetic
- Weaker theories of arithmetic