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Mathematical Logic (Math 570) Lecture Notes

Mathematical Logic (Math 570) Lecture NotesLou van den DriesFall Semester 2019 Contents1 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 .. 383 The Completeness Another Form of Completeness .. Proof of the Completeness Theorem .. Some Elementary Results of Predicate Logic .. Equational Classes and Universal algebra .. 544 Some Model L owenheim-Skolem; Vaught s Test .. Elementary Equivalence and Back-and-Forth .. Quantifier Elimination .. Presburger Arithmetic .. Skolemization and Extension by Definition.

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

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