Invitation to Mathematical Logic

David Marker is Professor Emeritus of Mathematics at the University of Illinois at Chicago where he was Liberal Arts & Sciences Distinguished Professor and a Fellow of the American Mathematical Society. His research interests lie in model theory and its applications. His textbook, Model Theory: An Introduction, which appeared as GTM 217 in 2002, was awarded the Association of Symbolic Logic Shoenfield Prize for expository writing.

• Introduction.- I. Truth and Proof.- 1 Languages, Structures and Theories.- 2 Embeddings and Substructures.- 3 Formal Proofs.- 4 Gödel's Completeness Theorem.- II. Elements of Model Theory.- 5 Compactness and Complete Theories.- 6 Ultraproducts.- 7 Quantifier Elimination.- 8 Model Theory of the Real Field.- III. Computability.- 9 Models of Computation.- 10 Universal Machines and Undecidability.- 11 Computably Enumerable and Arithmetic Sets.- 12 Turing Reducibility.-  IV. Arithmetic and Incompleteness.-13 Gödel's Incompleteness Theorems.- 14 Hilbert’s 10th Problem.- 15 Peano Arithmetic and ϵ0.- 16 Models of Arithmetic and Independence Results. - Appendices.- A Set Theory. - B Unique Readability. - C Real Algebra. -Bibliography. - Index.