TY  - GEN
AU  - Smullyan, Raymond M. 
TI  - The Godelian puzzle book: puzzles, paradoxes and proofs
SN  - 9780486497051
U1  - 793.74 SMU/G 
PY  - 2013///
CY  - New York
PB  - Dover Publications
KW  - Logic puzzles.
KW  - Mathematical recreations.
KW  - Godel's theorem.
N1  - Table of Contents

Part I: Puzzles, Paradoxes, Infinity and Other Curiosities
1. A Chatty Personal Introduction
2. Some Curious Adventures
3. The Strange Island of Musica
4. Four Metapuzzles
5. Certified Knights and Knaves
6. Paradoxical?
7. Infinity and Induction
8. Introducing Self-Reference
9. Fixed Point Puzzles
10. Some Curious Systems
11. How to Stump a Decision Machine
12. Some Additional Godelian Puzzles

Part II
13. Truth and Provability
14. Syntactic Incompleteness Theorems
15. Provability in Stages
16. Formal Systems and Recursion
17. Incompleteness and Undecidability
18. First-Order Arithmetic
19. Arithmetic Truth is Not Formalizable
20. The Incompleteness of Peano Arithmetic
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N2  - These brand-new recreational logic puzzles provide entertaining variations on Gödel's incompleteness theorems, offering ingenious challenges related to infinity, truth and provability, undecidability, and other concepts. Created by the celebrated logician Raymond Smullyan, the puzzles require no background in formal logic and will delight readers of all ages.

The two-part selection of puzzles and paradoxes begins with examinations of the nature of infinity and some curious systems related to Gödel's theorem. The first three chapters of Part II contain generalized Gödel theorems. Symbolic logic is deferred until the last three chapters, which give explanations and examples of first-order arithmetic, Peano arithmetic, and a complete proof of Gödel's celebrated result involving statements that cannot be proved or disproved. The book also includes a lively look at decision theory, better known as recursion theory, which plays a vital role in computer science
UR  - https://store.doverpublications.com/products/9780486497051?srsltid=AfmBOord5EJJ9IOFUGFtHFPKY9Vq12dvOzAQCv-B15lbe1y-8zrsNF-N
ER  -