A Ganzstellensatz for Semialgebraic Sets and a Boundedness Criterion for Rational Functions

REFERENCES

• Cherlin , G. ( 1976 ). Model theoretic algebra-selected topics. Lecture Notes in Mathematics 521. Berling-Heidelberg-New York: Springer-Verlang .
   Google Scholar
• Cherlin , G. , Dickmann , M. ( 1983 ). Real closed rings. II. Model theory . Ann. Pure Appl. Logic 25 ( 3 ): 213 – 231 .
   Web of Science ®Google Scholar
• Efrat , I. ( 2006 ). Valuations, orderings, and Milnor K-theory . Mathematical Surveys and Monographs . Vol. 124 . Providence : AMS .
   Google Scholar
• Haskell , D. , Yaffe , Y. ( 2008 ). Ganzstellensätze in theories of valued fields . J. Math. Logic 8 ( 1 ): 1 – 22 .
   Web of Science ®Google Scholar
• Haskell , D. , Yaffe , Y. Geometric Ganzstellensatz . Unpublished note .
   Google Scholar
• Kochen , S. Integer valued rational functions over the p-adic numbers: A p-adic analogue of the theory of real fields, 1969 . Number Theory (Proc. Sympos. Pure Math., Vol. XII, Houston, Tex., 1967) . Providence , R.I. : Amer. Math. Soc. , pp. 57 – 73 .
   Google Scholar
• Lavi , N. (2010). Ganzstellensatz for open sets over real closed valued fields. Master thesis, Ben Gurion University of the Negev.
   Google Scholar
• Plaumann , D. , Scheiderer , C. The ring of bounded polynomials on a semi-algebraic set . Transactions of the American Mathematical Society (2010) , To appear .
   Google Scholar
• Prestel , A. , Ripoll , C. ( 1991 ). Integral-valued rational functions on valued fields . Manuscripta Math. 73 : 437 – 452 .
   Web of Science ®Google Scholar
• Schweighofer , M. ( 2003 ). Iterated rings of bounded elements and generalizations of Schmüdgen's Positivstellensatz . J. Reine Angew. Math. 554 : 19 – 45 .
   Web of Science ®Google Scholar
• Communicated by A. Prestel.
   Google Scholar