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/lp/association-for-computing-machinery/a-proof-of-generalized-induction-7kPozWcDDv
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- Publisher
- Association for Computing Machinery
- Copyright
- Copyright © 1987 by ACM Inc.
- ISSN
- 0163-5700
- DOI
- 10.1145/24658.24660
- Publisher site
- See Article on Publisher Site
Abstract
A PROOF OF GENERALIZED INDUCTIO N Rod McBeth, London . Introductio n The purpose of the following is to expose the means b y which the theorem of generalized induction (introduce d as an axiom in [2] ) rests on the descending chai n condition, DCC, for the system EP . To save space, familiarity is assumed with the presentation s [21 L5] ; in particular with the discussion o f successor and diagonal polynomials . Notatio n denotes (1, 2, . . ) . IL is the functio n i (x) = 1, x e 7L + . Fundamental sequence s Let (EP, ) be the system of exponential function s ordered by eventual domination, given in [2] . Let ( , --~; ) be the lexicographically ordered syste m EP be diagonal . of finite trees of [51 . Let f Then using the order-conserving bijection T : EP-* of [5] , the standard LOB - WAINER assignment (ref . [l] , [7_1) of canonical fundamental sequences is given b y 1 DEFINITION ( n a + ) (f, n) = T -1 (T(f), n) . (via definition 4 .2 of [6] ) . Segments and
Journal
ACM SIGACT News – Association for Computing Machinery
Published: Apr 1, 1987