David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Studia Logica 77 (1):41 - 57 (2004)
Three systems of double extension set theory have been proposed by Andrzej Kisielewicz in two papers. In this paper, it is shown that the two stronger systems are inconsistent, and that the third, weakest system does not admit extensionality for general sets or the use of general sets as parameters in its comprehension scheme. The parameter-free version of the comprehension principle of double extension set theory is also shown to be inconsistent with extensionality. The definitions of the systems and a self-contained exposition of their properties is given, sufficient to develop the inconsistency proofs.
|Keywords||No keywords specified (fix it)|
|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
Jacob Lurie (1999). Anti-Admissible Sets. Journal of Symbolic Logic 64 (2):407-435.
Paul C. Gilmore (1986). Natural Deduction Based Set Theories: A New Resolution of the Old Paradoxes. Journal of Symbolic Logic 51 (2):393-411.
Keith Daynes (1989). Sets as Singularities in the Intensional Universe. Studia Logica 48 (1):111 - 128.
Masaru Shirahata (1996). A Linear Conservative Extension of Zermelo-Fraenkel Set Theory. Studia Logica 56 (3):361 - 392.
Stephen A. Fenner (1994). Almost Weakly 2-Generic Sets. Journal of Symbolic Logic 59 (3):868-887.
John Bell (2008). The Axiom of Choice and the Law of Excluded Middle in Weak Set Theories. Mathematical Logic Quarterly 54 (2):194-201.
F. A. Muller (2001). Sets, Classes, and Categories. British Journal for the Philosophy of Science 52 (3):539-573.
M. Randall Holmes (1995). The Equivalence of NF-Style Set Theories with "Tangled" Theories; the Construction of Ω-Models of Predicative NF (and More). Journal of Symbolic Logic 60 (1):178-190.
M. Randall Holmes (2005). The Structure of the Ordinals and the Interpretation of ZF in Double Extension Set Theory. Studia Logica 79 (3):357 - 372.
Sorry, there are not enough data points to plot this chart.
Added to index2009-01-28
Total downloads2 ( #372,030 of 1,139,819 )
Recent downloads (6 months)1 ( #172,630 of 1,139,819 )
How can I increase my downloads?