Mathematical Logic (Math 570) Lecture Notes

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Mathematical Logic (Math 570) Lecture NotesLou van den DriesFall Semester 2019Contents1 Mathematical Logic : a brief overview . . . . . . . . . . . . . . . . Sets and Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . .52 Basic Concepts of Propositional Logic . . . . . . . . . . . . . . . . . . . . . . . . . . Completeness for Propositional Logic . . . . . . . . . . . . . . . . Languages and Structures . . . . . . . . . . . . . . . . . . . . . . Variables and Terms . . . . . . . . . . . . . . . . . . . . . . . . . Formulas and Sentences . . . . . . . . . . . . . . . . . . . . . . . Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Logical Axioms and Rules; Formal Proofs.

the informal concepts it aims to capture, but no harm is done if this is kept rmly in mind. Example. The notorious Goldbach Conjecture asserts that every even integer greater than 2 is a sum of two prime numbers. With the understanding that the variables range over N = f0;1;2;:::g, and that 0;1;+;;< denote the

  Informal, Logic, Mathematical, Mathematical logic