A NOTE ON PREDICATIVE ORDINAL ANALYSIS I: ITERATED COMPREHENSION AND TRANSFINITE INDUCTION

Autor:	Sato Kentaro
Rok vydání:	2019
Předmět:	Logic 010102 general mathematics Ordinal analysis 0102 computer and information sciences 01 natural sciences Algebra Comprehension Philosophy Transfinite induction 010201 computation theory & mathematics Iterated function 0101 mathematics Predicative expression Mathematics
Zdroj:	The Journal of Symbolic Logic. 84:226-265
ISSN:	1943-5886 0022-4812
DOI:	10.1017/jsl.2017.71
Popis:	We determine the proof-theoretic ordinals (i) of ${\cal C} - {\bf{TI}}[\alpha ]$, the transfinite induction along α, for any hyperarithmetical level ${\cal C}$, in the first order setting and (ii) of any combination of iterated arithmetical comprehension and ${\cal C} - {\bf{TI}}[\alpha ]$ for ${\cal C}\, \equiv \,{\rm{\Pi }}_k^i ,{\rm{\Sigma }}_k^i$ ($i\, = \,0,1$) in the second order setting.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::5752db800472c68e68fdfa25e5a189d6 https://doi.org/10.1017/jsl.2017.71 Zobrazit plný text záznamu