This whole subfolder is about mathematical logic

  • Set theory
  • Model Theory
  • Proof theory
  • recursion theory

Well formed formula

Lowenheim Skolem For infinite models, there are always bigger and smaller models.

Lindstrom’s theorem Skolem’s paradox. Set theory says there are uncountable sets, but set theory is expressed in countable language

Semantic entailment

|= is used in different ways

G |= x. G is a set of formula. This is to say that every model in which G hold, x also holds

G, not x |= {} is unsat.


G |- x –> G |= x

Syntactic rules are obeyed in models.


G |= x –> G |- x


Infinite families of sentences


Incompleteness Theorem

Book list

mathematical logic through python