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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Propositional Logic and Other Fundamentals
Completeness and Compactness
9 other sections not shown
atomic formulas axioms binary binary relation Boolean algebra C-consistent class operation Clearly closed Compactness Theorem complete theory computation constant symbols construction contradiction Corollary decidable defined Definition denote effectively enumerable elementarily equivalent elementary substructure elements equivalent example exists extension finitely consistent first-order first-order logic follows formal free variables function F function symbol hence immediate induction hypothesis infinite cardinal intuitive isomorphic L-formula L-sentences L-structure L-theory language least Lemma limit ordinal marked at stage mathematical mk-i model 21 natural numbers non-logical symbols Note notion numbers ordinal otherwise particular preceding proposition primitive recursive primitive recursive function prove quantifier r.e. set recursive function recursive relation recursive set recursively axiomatizable recursively enumerable relation symbol result satisfied second-order logic Section set operation structure 21 substructure suffices Suppose T-representable tautology Th(fi transitive truth assignment ultrafilter unary uncountable unique verify weakly well-ordering ZF h