Logic MOC

Formal theory

A formal theory T in a formal language L is a set of distinguished formulae T ⊆L, logic which are typically interpreted as formulae which are true according to the theory and called theorems of the theory. There are two usual routes to constructing such a theory

1. Syntactic — T consists of all theorems of a given Formal system (L,I), i.e. T =Th⁡(L,I).
2. Semantic — T consists of formulae which are true of a given model or interpretation of L

Examples

• Syntactic
  • PA
  • Axiomatic set theory
  • Type theory

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