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Mathematical Logic - Exercises and Solutions (Hardcover, 1st ed. 2022)
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Mathematical Logic - Exercises and Solutions (Hardcover, 1st ed. 2022)
Series: Problem Books in Mathematics
Expected to ship within 12 - 17 working days
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This book gathers together a colorful set of problems on classical
Mathematical Logic, selected from over 30 years of teaching. The
initial chapters start with problems from supporting fields, like
set theory (ultrafilter constructions), full-information game
theory (strategies), automata, and recursion theory (decidability,
Kleene's theorems). The work then advances toward propositional
logic (compactness and completeness, resolution method), followed
by first-order logic, including quantifier elimination and the
Ehrenfeucht- Fraisse game; ultraproducts; and examples for
axiomatizability and non-axiomatizability. The Arithmetic part
covers Robinson's theory, Peano's axiom system, and Goedel's
incompleteness theorems. Finally, the book touches universal
graphs, tournaments, and the zero-one law in Mathematical Logic.
Instructors teaching Mathematical Logic, as well as students who
want to understand its concepts and methods, can greatly benefit
from this work. The style and topics have been specially chosen so
that readers interested in the mathematical content and methodology
could follow the problems and prove the main theorems themselves,
including Goedel's famous completeness and incompleteness theorems.
Examples of applications on axiomatizability and decidability of
numerous mathematical theories enrich this volume.
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