A Mathematical Introduction to LogicA Mathematical Introduction to Logic |
Contents
| 1 | |
| 11 | |
Chapter Two FirstOrder Logic | 67 |
Chapter Three Undecidability | 182 |
Chapter Four SecondOrder Logic | 282 |
SUGGESTIONS FOR FURTHER READING | 307 |
LIST OF SYMBOLS | 309 |
INDEX | 311 |
Common terms and phrases
a₁ Assume atomic formulas axiom group axiomatizable theory binary relation Boolean function cardinality Cn AE compactness theorem computable consistent constant symbols COROLLARY countable decidable deduction defined definition effectively enumerable elementarily equivalent example Exercise expression fact finite sequence first-order logic formal language function f function symbol Gödel number Hence infinite isomorphic lemma logical axioms Löwenheim-Skolem theorem many-sorted modus ponens n-place function natural numbers notation number theory obtained occur free one-to-one parameters partial function PROOF quantifier-free quantifiers real numbers recursive function recursive partial function recursively enumerable representable in Cn satisfies second-order Section 3.5 sentence symbols sentential logic set of Gödel set of sentences set theory Show soundness theorem structure suppose T₁ translated true truth assignment two-place predicate symbol universe v₁ valid variable Z-chains