Introduction To The Theory Of Logic
This book provides a rigorous introduction to the basic concepts and results of contemporary logic. It also presents, in two unhurried chapters, the mathematical tools (mainly from set theory) that are needed to master the technical aspects of the subject. Methods of definition and proof are also discussed at length, with special emphasis on inductive definitions and proofs and recursive definitions. The book is ideally suited for readers who want to undertake a serious study of logic but lack the mathematical background that other texts at this level presuppose. It can be used as a textbook in graduate and advanced undergraduate courses in logic. Hundreds of exercises are provided. Topics covered include basic set theory, propositional and first-order syntax and semantics, a sequent calculus-style deductive system, the soundness and completeness theorems, cardinality, the expressive limitations of first-order logic, with especial attention to the Loewenheim-Skolem theorems and non-standard models of arithmetic, decidability, complete theories, categoricity and quantifier elimination.
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admissible PL-assignment atomic truth assignment Axiom of Choice basic bigger than Venus binary relation brackets C-purge closed terms composition devices conjunct contains Continuum Hypothesis countable decimal expansion deducibility claim deductive system denotation denumerable disjunctive domain equivalence relation establish Exercise expressively complete extralogical symbols false finite set first-order language first-order logic first-order propositions free variables function pairing function symbol guage Hence Hint indiscernibility individual constants inductive clauses isomorphism Let/be logical consequence claims logically equivalent maximal element model the syntactic n-formulas natural number need to show Notice objects occur one-place one-to-one correspondence one-to-one function PL-sentence positive integer predicate proof of Lemma prove quantifier rational number represented result rule satisfies sequence set of formulas set of sentences suffice to show syntactic pattern Theorem tion true truth function truth value truth-functional tuple unique universe variable interpretation Vx Px well-rounded set Zorn's Lemma