Ordinal Diagrams for $\Pi_3$-Reflection
Arai, Toshiyasu
J. Symbolic Logic, Tome 65 (2000) no. 1, p. 1375-1394 / Harvested from Project Euclid
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In this paper we introduce a recursive notation system O($\Pi_3$) of ordinals. An element of the notation system is called an ordinal diagram. The system is designed for proof theoretic study of theories of $\Pi_3$-reflection. We show that for each $\alpha < \Omega$ in O($\Pi_3$) a set theory KP $\Pi_3$ for $\Pi_3$-reflection proves that the initial segment of O($\Pi_3$) determined by $\alpha$ is a well ordering. Proof theoretic study for such theories will be reported in [4].
Publié le : 2000-09-14
Classification:  
@article{1183746186,
     author = {Arai, Toshiyasu},
     title = {Ordinal Diagrams for $\Pi\_3$-Reflection},
     journal = {J. Symbolic Logic},
     volume = {65},
     number = {1},
     year = {2000},
     pages = { 1375-1394},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183746186}
}

Arai, Toshiyasu. Ordinal Diagrams for $\Pi_3$-Reflection. J. Symbolic Logic, Tome 65 (2000) no. 1, pp.  1375-1394. http://gdmltest.u-ga.fr/item/1183746186/