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] Jon Barwise, Admissible sets and structures, Springer-Verlag, Berlin, 1975. An approach to definability theory; Perspectives in Mathematical Logic. MR 0424560 (54 #12519)
  • [2] Jon Barwise and John Schlipf, On recursively saturated models of arithmetic, Model theory and algebra (A memorial tribute to Abraham Robinson), Springer, Berlin, 1975, pp. 42–55. Lecture Notes in Math., Vol. 498. MR 0409172 (53 #12934)
  • [3] H. Jerome Keisler, Models with tree structures, Proceedings of the Tarski Symposium (Proc. Sympos. Pure Math., Vol. XXV, Univ. California, Berkeley, Calif., 1971), 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