David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Philosophical Logic 37 (2):121 - 140 (2008)
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.
|Keywords||axiom of foundation quantifier complexity weak set theory|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library||
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Thomas Glass (1996). On Power Set in Explicit Mathematics. Journal of Symbolic Logic 61 (2):468-489.
Richard Pettigrew (2009). On Interpretations of Bounded Arithmetic and Bounded Set Theory. Notre Dame Journal of Formal Logic 50 (2):141-152.
Steve Awodey, Henrik Forssell & Michael A. Warren, Algebraic Models of Sets and Classes in Categories of Ideals.
Aleksandar Ignjatović (1995). Delineating Classes of Computational Complexity Via Second Order Theories with Weak Set Existence Principles. I. Journal of Symbolic Logic 60 (1):103-121.
Michael Rathjen (1992). A Proof-Theoretic Characterization of the Primitive Recursive Set Functions. Journal of Symbolic Logic 57 (3):954-969.
Athanassios Tzouvaras (2003). An Axiomatization of 'Very' Within Systiems of Set Theory. Studia Logica 73 (3):413 - 430.
David Asperó (2002). A Maximal Bounded Forcing Axiom. Journal of Symbolic Logic 67 (1):130-142.
John Bell (2008). The Axiom of Choice and the Law of Excluded Middle in Weak Set Theories. Mathematical Logic Quarterly 54 (2):194-201.
Added to index2009-01-28
Total downloads2 ( #258,437 of 1,089,079 )
Recent downloads (6 months)0
How can I increase my downloads?