منابع مشابه
On Exponentially Closed Fields1
It is well known [4] that the non-Archimedean residue class fields K of the ring of continuous real valued functions on a space are realclosed and 7/i-sets. It does not appear to be known that the exponential function in the reals induces an exponential function in K (definitions to follow) ; thus K is exponentially closed. The property of being exponentially closed is a new invariant which wil...
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The notion of ‘Pseudo Algebraically Closed (PAC) extensions’ is a generalization of the classical notion of PAC fields. In this work we develop a basic machinery to study PAC extensions. This machinery is based on a generalization of embedding problems to field extensions. The main goal is to prove that the Galois closure of any proper separable algebraic PAC extension is its separable closure....
متن کاملLiouville Closed H-fields
H-fields are fields with an ordering and a derivation subject to some compatibilities. (Hardy fields extending R and fields of transseries over R are H-fields.) We prove basic facts about the location of zeros of differential polynomials in Liouville closed H-fields, and study various constructions in the category of H-fields: closure under powers, constant field extension, completion, and buil...
متن کاملReal closed exponential fields
In an extended abstract [20], Ressayre considered real closed exponential fields and integer parts that respect the exponential function. He outlined a proof that every real closed exponential field has an exponential integer part. In the present paper, we give a detailed account of Ressayre’s construction. The construction becomes canonical once we fix the real closed exponential field R, a re...
متن کاملDistribution of Periods of Closed Trajectories in Exponentially Shrinking Intervals
For hyperbolic flows over basic sets we study the asymptotic of the number of closed trajectories γ with periods Tγ lying in exponentially shrinking intervals (x−e−δx, x+ e), δ > 0, x → +∞. A general result is established which concerns hyperbolic flows admitting symbolic models whose corresponding Ruelle transfer operators satisfy some spectral estimates. This result applies to a variety of hy...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1962
ISSN: 0002-9939
DOI: 10.2307/2034159