Gödel's Theorems and Zermelo's Axioms

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The book offers a thorough introduction to the foundations of mathematics, beginning with essential concepts in mathematical logic, including axioms and model theory. It progresses to detailed proofs of Gödel's completeness and incompleteness theorems, emphasizing the impossibility of proving arithmetic consistency within its own axioms. The final section introduces modern axiomatic set theory based on Zermelo's axioms and Gödel's constructible universe. Throughout, it explores both standard and non-standard models of various mathematical theories, including Peano and Presburger arithmetic.