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.

we see their work as leading to boolean algebra, set theory, propositional logic, predicate logic, as clarifying the foundations of the natural and real number systems, and as introducing suggestive symbolic notation for logical operations. Also, their activity led to the view that logic + set theory can serve as a basis for 1

  Logic, Mathematical, Boolean, Algebra, Mathematical logic, Boolean algebra