Translations of Mathematical Monographs 1993; 153 pp; hardcover Volume: 128 ISBN10: 0821845764 ISBN13: 9780821845769 List Price: US$75 Member Price: US$60 Order Code: MMONO/128
 The aim of this work is to develop the tool of logical deduction schemata and use it to establish upper and lower bounds on the complexity of proofs and their transformations in axiomatized theories. The main results are establishment of upper bounds on the elongation of deductions in cut eliminations; a proof that the length of a direct deduction of an existence theorem in the predicate calculus cannot be bounded above by an elementary function of the length of an indirect deduction of the same theorem; a complexity version of the existence property of the constructive predicate calculus; and, for certain formal systems of arithmetic, restrictions on the complexity of deductions that guarantee that the deducibility of a formula for all natural numbers in some finite set implies the deducibility of the same formula with a universal quantifier over all sufficiently large numbers. Readership Research mathematicians. Table of Contents  Introduction
 Upper bounds on deduction elongation in cut elimination
 Systems of term equations with substitutions
 Logical deduction schemata in axiomatized theories
 Bounds for the complexity of terms occurring in proofs
 Proof strengthening theorems
 References
