List of model-theory notes:

• Positive and conditional sentences
• Free variables
• Logical Axioms and Rules of Inference
• Possible sets of all models
• Interpolation Theorem
• Satisfaction in First-order Logic
• Relationships between models
• Notation for First-order Logic
• Axiomatization in Sentential Logic
• Model Topology
• Syntax and Semantics
• Model Theory for Sentential Logic
• Model Theory for First-order Logic
• Consistency and Satisfiability
• Definable elements
• Notation for Sentential Logic
• Universal and Existential statements
• Examples of elementarily equivalent models
• Ehrenfeucht-Fraisse Game
• Generated submodel
• Completeness theorems
• Zermelo-Frankel Axioms
• Boolean algebra
• Definability in total orders
• Lindenbaum algebra
• Löwenheim-Skolem-Tarski Theorems
• Set of witnesses
• Theories of order
• Filters and ultrafilters
• P-name hierarchy
• Transitive model
• Adding definitions to models
• Countable chain condition
• Peano Arithmetic
• Generic extension model of ZFC
• Fundamental Theorem of Forcing
• Forcing not-CH
• Weaker theories of arithmetic
• Forcing notion
• Continuum Hypothesis
• Ultraproduct
• Category of models
• Real closed field
• Model Theory for Modal Logic
• Axiom schemas in modal logic
• Type in model theory
• Realizing and omitting sets of formulas
• Finite intersection property
• Kripke semantics
• Algebraic system