Combinatorial principles in second-order theories of bounded arithmetic

An attempt is made to study the mathematical strength of the weak second order theories of Bounded Arithmetic U$\sbsp{2}{i}$ and V$\sbsp{2}{i}$, i $\geq$ 0, introduced by S. Buss. It is first shown that U$\sbsp{2}{1}$ can $\Sigma\sbsp{1}{1,b}$-define the functions in the second class of Grzegorczyk, $\varepsilon\sp2$, or, equivalently, the class of $\Sigma\sbsp{1}{1,b}$-definable functions in U$\sbsp{2}{1}$ is closed under bounded recursion.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• De Castro, Rodrigo

Contributors dc:contributor

• Jockusch, Carl G., Jr.

• Mathematics

Statement dc:rights

• Copyright 1992 De Castro, Rodrigo

Language dc:language

eng

Identifier

AAI9236438
(UMI)AAI9236438

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/20320