Mathematical Logic

Part I: Logic, Sets, and Numbers.- Chapter 1. First-order Logic.- Chapter 2. Logical seeing.- Chapter 3. What is a Number?.- Chapter 4. Seeing the Number Structures.- Chapter 5. Points, Lines, and the Structure of R.- Chapter 6. Set Theory.- Part II: Relations, Structures, Geometry.- Chapter 7. Relations.- Chapter 8. Definable Elements and Constants.- Chapter 9. Minimal and Order-Minimal Structures.- Chapter 10. Geometry of Definable Sets.- Chapter 11. Where Do Structures Come From?.- Chapter 12. Elementary Extensions and Symmetries.- Chapter 13. Tame vs. Wild.- Chapter 14. First-Order Properties.- Chapter 15. Symmetries and Logical Visibility One More Time.- Part III: Inference, Models, Categoricity and Diversity.- Chapter 16. Logical Inference.- Chapter 17. Categoricity.- Chapter 18. Counting Countable Models.- Chapter 19. Infinitary Logics.- Chapter 20. Symmetry and Definability.- Appendices.- Bibliography.- Index.

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• Hardware do computador
• Filosofia da Matemátuca
• Lógica matemática
• Filosofia: a lógica
• Matemática aplicada

first-order logic introduction;Abstract symmetries;Number system development;Model theory;Formal arithmetic;Tameness mathematical structures;Axiomatic set theory;Compactness Theorem;Logical visibility;first-order logic applications;complexity mathematical structures;Applied compactness theorem;geometry definable sets;mathematical structure relations;logical visibility;language of modern mathematics;recent developents model theory;Ramsey theory