ENGLISH

Complexity of Proofs and Their Transformations in Axiomatic Theories

By V. P. Orevkov

Book information

Publisher
American Mathematical Society
Year
1993
ISBN
0821845764, 9780821845769
Language
english
Format
DJVU
Filesize
2 MB (1684789 bytes)
Series
Translations of Mathematical Monographs
Pages
153\164
DPI
600
Time added
2014-03-07 15:42:31

Description

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.

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