Fundamentals of Mathematical Logic
This introductory graduate text covers modern mathematical logic from propositional, first-order and infinitary logic and Gödel's Incompleteness Theorems to extensive introductions to set theory, model theory and recursion (computability) theory. Based on the author's more than 35 years of teaching experience, the book develops students' intuition by presenting complex ideas in the simplest context for which they make sense. The book is appropriate for use as a classroom text, for self-study, and as a reference on the state of modern logic.
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algebra assignment assume atomic axiomatizable axioms Boolean called cardinal Chapter Clearly closed Compactness complete computation condition consider consistent constant symbols construction Corollary countable course decidable defined Definition denote easily effectively elements enumerable equivalent establish exactly example Exercise exists expressions extension fact Finally finite follows formal formula function function F give given hence holds hypothesis immediate induction infinite interpretable isomorphic L-sentences language least Lemma logic marked mathematical natural Note notion numbers ordering otherwise partial particular preceding Proof Proposition prove recursive recursive function relation result satisfied sentence sequence set operation simple stage structure subset Suppose symbols Theorem theory transitive true truth unique universe variables verify write