Graduate studies at Western
Journal of Symbolic Logic 66 (3):1321-1341 (2001)
|Abstract||We present an axiomatic framework for nonstandard analysis-the Nonstandard Class Theory (NCT) which extends von Neumann-Gödel-Bernays Set Theory (NBG) by adding a unary predicate symbol St to the language of NBG (St(X) means that the class X is standard) and axioms-related to it- analogs of Nelson's idealization, standardization and transfer principles. Those principles are formulated as axioms, rather than axiom schemes, so that NCT is finitely axiomatizable. NCT can be considered as a theory of definable classes of Bounded Set Theory by V. Kanovei and M. Reeken. In many aspects NCT resembles the Alternative Set Theory by P. Vopenka. For example there exist semisets (proper subclasses of sets) in NCT and it can be proved that a set has a standard finite cardinality iff it does not contain any proper subsemiset. Semisets can be considered as external classes in NCT. Thus the saturation principle can be formalized in NCT|
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
Mauro Di Nasso (2002). An Axiomatic Presentation of the Nonstandard Methods in Mathematics. Journal of Symbolic Logic 67 (1):315 - 325.
John P. Burgess (2004). E Pluribus Unum: Plural Logic and Set Theory. Philosophia Mathematica 12 (3):193-221.
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.
Vladimir Kanovei & Michael Reeken (1996). Internal Approach to External Sets and Universes. Studia Logica 56 (3):293 - 322.
William M. Farmer & Joshua D. Guttman (2000). A Set Theory with Support for Partial Functions. Studia Logica 66 (1):59-78.
Paul E. Howard, Arthur L. Rubin & Jean E. Rubin (1978). Independence Results for Class Forms of the Axiom of Choice. Journal of Symbolic Logic 43 (4):673-684.
Petr Andreev & Karel Hrbacek (2004). Standard Sets in Nonstandard Set Theory. Journal of Symbolic Logic 69 (1):165-182.
Vladimir Kanovei & Michael Reeken (1998). Elementary Extensions of External Classes in a Nonstandard Universe. Studia Logica 60 (2):253-273.
Peter Fletcher (1989). Nonstandard Set Theory. Journal of Symbolic Logic 54 (3):1000-1008.
Added to index2009-01-28
Total downloads6 ( #154,793 of 739,318 )
Recent downloads (6 months)1 ( #61,243 of 739,318 )
How can I increase my downloads?