LÉVY HIERARCHY IN WEAK SET THEORIES

LÉVY HIERARCHY IN WEAK SET THEORIES

We investigate the interactions of formula complexity in weak set theories with the axioms available there. In particular, we show that swapping bounded and unbounded quantification preserves formula complexity in presence of the axiom of foundation weakened to an arbitrary set base, while it does n...

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Veröffentlicht in:Journal of philosophical logic 2008-04, Vol.37 (2), p.121-140
1. Verfasser: HANIKA, JIŘÍ
Format: Artikel
Sprache:eng
Schlagworte:
Axiom of choice
Axiom schema of replacement
Axioms
Education
Logic
Mathematical functions
Mathematical logic
Mathematical set theory
Mathematical transitivity
Mathematics
Philosophical axioms
Philosophy
Principles
Quantification
Set theory
Variables
Zermelo Frankel set theory
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Beschreibung
Zusammenfassung:We investigate the interactions of formula complexity in weak set theories with the axioms available there. In particular, we show that swapping bounded and unbounded quantification preserves formula complexity in presence of the axiom of foundation weakened to an arbitrary set base, while it does not if the axiom of foundation is further weakened to a proper class base. More attention is being paid to the necessary axioms employed in the positive results, than to the combinatorial strength of the positive results themselves.
ISSN:0022-3611
1573-0433
DOI:10.1007/s10992-007-9063-1