The Strength of Replacement in Weak Arithmetic (2003)
by
Stephen Cook
,
Neil Thapen
| Citations: | 10 - 3 self |
BibTeX
@MISC{Cook03thestrength,
author = {Stephen Cook and Neil Thapen},
title = {The Strength of Replacement in Weak Arithmetic},
year = {2003}
}
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Abstract
The replacement (or collection or choice) axiom scheme BB() asserts bounded quanti er exchange as follows: 8i< jaj 9x<a(i;x) ! 9w 8i< jaj (i; [w] i ) where is in the class of formulas. The theory S 2 proves the scheme BB( 1 ), and thus in S 2 every 1 formula is equivalent to a strict formula (in which all non-sharply-bounded quanti ers are in front).
