David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Archive for Mathematical Logic 41 (6):581-602 (2002)
Using a slight generalization, due to Palmgren, of sheaf semantics, we present a term-model construction that assigns a model to any first-order intuitionistic theory. A modification of this construction then assigns a nonstandard model to any theory of arithmetic, enabling us to reproduce conservation results of Moerdijk and Palmgren for nonstandard Heyting arithmetic. Internalizing the construction allows us to strengthen these results with additional transfer rules; we then show that even trivial transfer axioms or minor strengthenings of these rules destroy conservativity over HA. The analysis also shows that nonstandard HA has neither the disjunction property nor the explicit definability property. Finally, careful attention to the complexity of our definitions allows us to show that a certain weak fragment of intuitionistic nonstandard arithmetic is conservative over primitive recursive arithmetic.
|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
Benno van den Berg, Eyvind Briseid & Pavol Safarik (2012). A Functional Interpretation for Nonstandard Arithmetic. Annals of Pure and Applied Logic 163 (12):1962-1994.
Carsten Butz (2004). Saturated Models of Intuitionistic Theories. Annals of Pure and Applied Logic 129 (1-3):245-275.
Similar books and articles
Daniel Dzierzgowski (1995). Models of Intuitionistic TT and N. Journal of Symbolic Logic 60 (2):640-653.
Kenneth McAloon (1982). On the Complexity of Models of Arithmetic. Journal of Symbolic Logic 47 (2):403-415.
Andreas Blass (1974). On Certain Types and Models for Arithmetic. Journal of Symbolic Logic 39 (1):151-162.
Michael Potter (1998). Classical Arithmetic as Part of Intuitionistic Arithmetic. Grazer Philosophische Studien 55:127-41.
Stuart T. Smith (1987). Nonstandard Characterizations of Recursive Saturation and Resplendency. Journal of Symbolic Logic 52 (3):842-863.
Chris Mortensen (1987). Inconsistent Nonstandard Arithmetic. Journal of Symbolic Logic 52 (2):512-518.
Erik Palmgren (1998). Developments in Constructive Nonstandard Analysis. Bulletin of Symbolic Logic 4 (3):233-272.
C. Ward Henson, Matt Kaufmann & H. Jerome Keisler (1984). The Strength of Nonstandard Methods in Arithmetic. Journal of Symbolic Logic 49 (4):1039-1058.
H. Jerome Keisler (2006). Nonstandard Arithmetic and Reverse Mathematics. Bulletin of Symbolic Logic 12 (1):100-125.
Added to index2009-01-28
Total downloads37 ( #73,446 of 1,699,830 )
Recent downloads (6 months)9 ( #69,042 of 1,699,830 )
How can I increase my downloads?