Mathematical logic, Formal system, Model theory

• Propositional logic
• First-order logic
• Second-order logic
• Higher-order logic (equivalent to second-order)

https://www.lesswrong.com/posts/SWn4rqdycu83ikfBa/second-order-logic-the-controversy

an intro to logic videos

Boolean algebra

clauses,

open propositions, with free vairables == Property

closed formulas with quantified variables == truths or falsities

Quantifiers

• Existence
• Universality

A variable under the dominion of a quantifier is called a quantified variable.

The game of logic, by Lewis Carroll