David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 61 (2):586-607 (1996)
We prove that a necessary and sufficient condition for a countable set L of sets of integers to be equal to the algebra of all sets of integers definable in a nonstandard elementary extension of ω by a formula of the PA language which may include the standardness predicate but does not contain nonstandard parameters, is as follows: L is closed under arithmetical definability and contains 0 (ω) , the set of all (Gödel numbers of) true arithmetical sentences. Some results related to definability of sets of integers in elementary extensions of ω are included
|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.
C. Ward Henson, Matt Kaufmann & H. Jerome Keisler (1984). The Strength of Nonstandard Methods in Arithmetic. Journal of Symbolic Logic 49 (4):1039-1058.
Andrew Arana (2001). Solovay's Theorem Cannot Be Simplified. Annals of Pure and Applied Logic 112 (1):27-41.
Chris Mortensen (1987). Inconsistent Nonstandard Arithmetic. Journal of Symbolic Logic 52 (2):512-518.
George Mills (1978). A Model of Peano Arithmetic with No Elementary End Extension. Journal of Symbolic Logic 43 (3):563-567.
Kenneth McAloon (1982). On the Complexity of Models of Arithmetic. Journal of Symbolic Logic 47 (2):403-415.
Stuart T. Smith (1987). Nonstandard Characterizations of Recursive Saturation and Resplendency. Journal of Symbolic Logic 52 (3):842-863.
Vladimir Kanovei & Michael Reeken (2000). Extending Standard Models of ZFC to Models of Nonstandard Set Theories. Studia Logica 64 (1):37-59.
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.
Sorry, there are not enough data points to plot this chart.
Added to index2009-01-28
Total downloads1 ( #483,801 of 1,413,361 )
Recent downloads (6 months)0
How can I increase my downloads?