دانلود کتاب اثبات‌های صوری در نظریه مجموعه‌های مقدماتی – قوانین منطق برای اثبات‌های صوری در نظریه مجموعه‌های زرملو

A formal proof is a proof that is mechanically verifiable. The book gives the details of how to write a formal proof. The book gives formal proofs of theorems in set theory that is commonly employed as a foundation for the whole of mathematics. The Zermelo axiom system is chosen as the basis for set theory. The Zermelo axioms are sufficient for the topics covered in this book. The first chapter of the book gives the rules of logic required to write formal proofs. It is assumed that the reader has basic knowledge of logic. A detailed justification of the rules of logic can be found in some of the references given at the end of the chapter. The second chapter of the book gives formal proofs of theorems in elementary set theory. It includes a proof of the existence of a Peano system that provides a foundation for the number theory. The reader is expected to know what “axiomatic set theory” is. The book helps the reader to write formal proofs. The book can serve as a reference for a course that covers “formal proofs” or “formal proofs in set theory.” The book can be used to develop a software that can be used to verify formal proofs.