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A note on the theory SID < ω of stratified induction
Author(s) -
Ranzi Florian,
Strahm Thomas
Publication year - 2014
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201300063
Subject(s) - finitary , mathematics , discrete mathematics , mathematical economics , pure mathematics , calculus (dental) , medicine , dentistry
We introduce and analyse a theory of finitely stratified general inductive definitions over the natural numbers, SID < ω , and establish its proof theoretic ordinal,φ ɛ 0( 0 ) . The definition of SID < ωbears some similarities with Leivant's ramified theories for finitary inductive definitions.