David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Studia Logica 56 (3):293 - 322 (1996)
In this article we show how the universe of HST, Hrbaek set theory (a nonstandard set theory of external type, which includes, in particular, the ZFC Replacement and Separation schemata for all formulas in the language containing the membership and standardness predicates, and Saturation for standard size families of internal sets, but does not include the Power set axiom) admits a system of subuniverses which keep the Replacement, model Power set and Choice (in fact all of ZFC, with the exception of the Regularity axiom, which indeed is replaced by the Regularity over the internal subuniverse), and also keep as much of Saturation as it is necessary.This gives sufficient tools to develop the most complicated topics in nonstandard analysis, such as Loeb measures.
|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
Vladimir Kanovei & Michael Reeken (1998). Elementary Extensions of External Classes in a Nonstandard Universe. Studia Logica 60 (2):253-273.
Mauro Di Nasso (2002). An Axiomatic Presentation of the Nonstandard Methods in Mathematics. Journal of Symbolic Logic 67 (1):315 - 325.
Siegfried Gottwald (2006). Universes of Fuzzy Sets and Axiomatizations of Fuzzy Set Theory. Part I: Model-Based and Axiomatic Approaches. [REVIEW] Studia Logica 82 (2):211 - 244.
Mauro Di Nasso (1998). Pseudo-Superstructures as Nonstandard Universes. Journal of Symbolic Logic 63 (1):222 - 236.
Vladimir Kanovei (1996). On External Scott Algebras in Nonstandard Models of Peano Arithmetic. Journal of Symbolic Logic 61 (2):586-607.
V. Kanovei (1995). Uniqueness, Collection, and External Collapse of Cardinals in Ist and Models of Peano Arithmetic. Journal of Symbolic Logic 60 (1):318-324.
Vladimir Kanovei & Michael Reeken (2000). Extending Standard Models of ZFC to Models of Nonstandard Set Theories. Studia Logica 64 (1):37-59.
Arnold W. Miller (1990). Set Theoretic Properties of Loeb Measure. Journal of Symbolic Logic 55 (3):1022-1036.
Vladimir Kanovei & Michael Reeken (1995). Internal Approach to External Sets and Universes. Studia Logica 55 (2):347 - 376.
P. V. Andreev & E. I. Gordon (2001). An Axiomatics for Nonstandard Set Theory, Based on Von Neumann-Bernays-Gödel Theory. Journal of Symbolic Logic 66 (3):1321-1341.
Added to index2009-01-28
Total downloads5 ( #256,056 of 1,410,134 )
Recent downloads (6 months)1 ( #177,743 of 1,410,134 )
How can I increase my downloads?