Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A rather classless model


Author: Matt Kaufmann
Journal: Proc. Amer. Math. Soc. 62 (1977), 330-333
MSC: Primary 02H20
MathSciNet review: 0476498
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Using $ {\diamondsuit _{{\omega _1}}}$, a model $ \mathfrak{N}$ of Peano arithmetic is constructed which has a unique extension $ (\mathfrak{N},\chi )$ to a model of $ \Delta _1^1$-PA, Peano arithmetic with $ \Delta _1^1$-comprehension.


References [Enhancements On Off] (What's this?)

  • [1] K. J. Barwise, Admissible sets and structures, Springer-Verlag, Heidelberg, 1975. MR 0424560 (54:12519)
  • [2] K. J. Barwise and J. Schlipf, On recursively saturated models of arithmetic, Model Theory and Algebra, Lecture Notes in Math., vol. 498, Springer-Verlag, Berlin, 1976, 42-55. MR 0409172 (53:12934)
  • [3] H. J. Keisler, Models with tree structures, Proc. Tarski Sympos., Proc. Sympos. Pure Math., Amer. Math. Soc., Providence, R.I., 1974, pp. 331-348. MR 0357108 (50:9576)
  • [4] J. Schlipf, Some hyperelementary aspects of model theory, Doctoral Dissertation, University of Wisconsin, Madison, Wis., 1975.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 02H20

Retrieve articles in all journals with MSC: 02H20


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0476498-7
PII: S 0002-9939(1977)0476498-7
Keywords: Recursively saturated model, Peano arithmetic, $ \Delta _1^1$-comprehension, $ {\diamondsuit _{{\omega _1}}}$, Barwise Compactness Theorem, Barwise Completeness Theorem, $ HY{P_\mathfrak{N}}$, $ KP{U^ + }$
Article copyright: © Copyright 1977 American Mathematical Society