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Model theory of analytic functions: some historical comments

Deirdre Haskell

Bulletin of Symbolic Logic 18 (3):368-381 (2012)

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Pseudo-exponentiation on algebraically closed fields of characteristic zero.Boris Zilber - 2005 - Annals of Pure and Applied Logic 132 (1):67-95.details We construct and study structures imitating the field of complex numbers with exponentiation. We give a natural, albeit non first-order, axiomatisation for the corresponding class of structures and prove that the class has a unique model in every uncountable cardinality. This gives grounds to conjecture that the unique model of cardinality continuum is isomorphic to the field of complex numbers with exponentiation. Logic and Philosophy of Logic, Miscellaneous in Logic and Philosophy of Logic Model Theory in Logic and Philosophy of Logic Science, Logic, and Mathematics Direct download (6 more) Export citation Bookmark 28 citations
A Decision Method for Elementary Algebra and Geometry.Alfred Tarski - 1952 - Journal of Symbolic Logic 17 (3):207-207.details Logic and Philosophy of Logic Direct download Export citation Bookmark 75 citations
A Decision Method for Elementary Algebra and Geometry.Alfred Tarski - 1949 - Journal of Symbolic Logic 14 (3):188-188.details Logic and Philosophy of Logic Direct download Export citation Bookmark 71 citations
Imaginaries in real closed valued fields.Timothy Mellor - 2006 - Annals of Pure and Applied Logic 139 (1):230-279.details The paper shows elimination of imaginaries for real closed valued fields to suitable sorts. We also show that this result is in some sense optimal. The paper includes a quantifier elimination theorem for real closed valued fields in a language with sorts for the field, value group and residue field. Model Theory in Logic and Philosophy of Logic Science, Logic, and Mathematics Direct download (4 more) Export citation Bookmark 9 citations
On definable subsets of p-adic fields.Angus MacIntyre - 1976 - Journal of Symbolic Logic 41 (3):605-610.details Logic and Philosophy of Logic Model Theory in Logic and Philosophy of Logic Direct download (9 more) Export citation Bookmark 25 citations
The theory of liouville functions.Pascal Koiran - 2003 - Journal of Symbolic Logic 68 (2):353-365.details A Liouville function is an analytic function $H : C \rightarrow C$ with a Taylor series $\Sigma_{n=1}^\infty x^n/a_n$ such the $a_n\prime s$ form a "very fast growing" sequence of integers. In this paper we exhibit the complete first-order theory of the complex field expanded with H. Blaise Pascal in 17th/18th Century Philosophy Logic and Philosophy of Logic Direct download (10 more) Export citation Bookmark 3 citations
A Remark on Zilber's Pseudoexponentiation.David Marker - 2006 - Journal of Symbolic Logic 71 (3):791 - 798.details Logic and Philosophy of Logic Model Theory in Logic and Philosophy of Logic Direct download (5 more) Export citation Bookmark 5 citations
The theory of Liouville functions.Pascal Koiran - 2003 - Journal of Symbolic Logic 68 (2):353-365.details A Liouville function is an analytic function $H: \C \rightarrow \C$ with a Taylor series $\sumn=1\infty xn/an$ such the an’s form a “very fast growing” sequence of integers. In this paper we exhibit the complete first-order theory of the complex field expanded with H. Logic and Philosophy of Logic Direct download Export citation Bookmark 3 citations
On the decidability of the real exponential field.Angus Macintyre & Alex J. Wilkie - 1996 - In Piergiorgio Odifreddi (ed.), Kreiseliana. About and Around Georg Kreisel. A K Peters. pp. 441--467.details Areas of Mathematics in Philosophy of Mathematics $160.00 used (collection) View on Amazon.com Export citation Bookmark 14 citations

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