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On Overspill Principles and Axiom Schemes for Bounded Formulas
Author(s) -
BorregoDíaz Joaquín,
FernándezMargarit Alejandro,
PérezJiménez Mario
Publication year - 1996
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.19960420129
Subject(s) - axiom , bounded function , mathematics , scheme (mathematics) , subject (documents) , discrete mathematics , combinatorics , mathematical economics , computer science , mathematical analysis , geometry , library science
We study the theories I∇ n , L∇ n and overspill principles for ∇ n formulas. We show that IE n ⇒ L∇ n ⇒ I∇ n , but we do not know if I∇ n L∇ n . We introduce a new scheme, the growth scheme Crγ, and we prove that L∇ n ⇒ Cr∇ n ⇒ I∇ n . Also, we analyse the utility of bounded collection axioms for the study of the above theories. Mathematics Subject Classification: 03F30, 03H15.