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The Foundations of Mathematics

The Foundations of Mathematicsc 2005,2006,2007 Kenneth KunenKenneth KunenOctober 29, 2007 Contents0 Prerequisites .. Logical Notation .. Why Read This Book? .. The Foundations of Mathematics ..5I Set .. Axioms .. Remarks on Presentation.. theory is the theory of everything .. , Comprehension, Pairing, Union .. , Functions, Discrete Mathematics .. Remarks .. and Recursion on the Ordinals .. Power Sets .. Cardinals .. The Axiom of Choice (AC) .. Cardinal Arithmetic .. The Axiom of Foundation .. Real Numbers and Symbolic Entities ..73II Model Theory and Proof Plan .. Historical introduction to Proof Theory.

Introduction 0.1 Prerequisites It is assumed that the reader knows basic undergraduate mathematics. Specifically: You should feel comfortable thinking about abstract mathematical structures such as groups and fields. You should also …

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