Invitation to Mathematical Logic

Inbunden, Engelska, 2024

Av David Marker

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The material should be accessible to first year graduate students or advanced undergraduates in mathematics, graduate students in philosophy with a solid math background, or students in computer science who want a mathematical introduction to logic.

Produktinformation

Utgivningsdatum2024-05-07
Mått155 x 235 x 25 mm
Vikt802 g
FormatInbunden
SpråkEngelska
SerieGraduate Texts in Mathematics
Antal sidor357
FörlagSpringer International Publishing AG
ISBN9783031553677

Tillhör följande kategorier

Matematikens grunder inom Naturvetenskap och teknik

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.