数理逻辑(第2版 英文影印版)

.　7.some remarks on formalizability
　8.substitution
ⅳ a sequent calculus
1．sequent rules
2．structural rules and connective rules
3．derivable connective rules
4．quantifier and equality rules
5．further derivable rules and sequents
6．summary and example
7．consistency
ⅴthe completeness theorem
1．henkin’s theorem．
2． satisfiability of consistent sets of formulas（the countable casel
3． satisfiability of consistent sets of formulas（the general case）
4．the completeness theorem
ⅵ the lswenheim-skolem and the compactness theorem
1．the l6wenheim-skolem theorem．
2．the compactness theorem
3．elementary classes
4．elementarily equivalent structures
ⅶ the scope of first-order logic
1．the notion of formal proof
2．mathematics within the framework of fimt—order logic
3．the zermelo-fraenkel axioms for set theory．
4．set theory as a basis for mathematics
ⅷ syntactic interpretations and normal forms
1．term-reduced formulas and relational symbol sets
2．syntactic interpretations
3．extensions by definitions
4．normal forms
part b
ⅸ extensions of first-order logic
ⅹ limitations of the formal method
? free models and logic programming
? an algebraic characterization of elementary equivalence
ⅹⅲ lindstrom’s theorems
references
symbol index
subject index