Mirqāt The Ascent of Logic

Intermediate · a field of logic

Mathematical Logic

Model theory, computability, and recursion: logic turned on mathematics, and the limits Gödel and Tarski revealed.

The problem
Exactly how much can a formal system prove about itself, and where do truth, proof, and computation part ways?
The turning point
Gödel’s first incompleteness theorem: any consistent, sufficiently strong system has a true sentence it cannot prove.
An open question
How do the model-theoretic dividing lines (stability, NIP) organize all of mathematics, and how far do they reach?

The Canon

  • Gödel On Formally Undecidable Propositions 1931
  • Tarski The Concept of Truth in Formalized Languages 1933
  • Boolos, Burgess & Jeffrey Computability and Logic

To study it

  • Bell & Machover A Course in Mathematical Logic
  • Marker Model Theory: An Introduction
  • Chang & Keisler Model Theory
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