Ultraproducts Of O Minimal Structures PDF Download
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Author | : Alex Rennet |
Publisher | : |
Total Pages | : 178 |
Release | : 2012 |
Genre | : |
ISBN | : |
Download Ultraproducts of O-Minimal Structures Book in PDF, ePub and Kindle
There are three main parts to this thesis, all centred around ultraproducts of o-minimal structures. In the first part we investigate (for a fixed first-order language L) what we call the L-theory of o-minimality. It is the theory consisting of those L-sentences true in all o-minimal L-structures. We find that when L expands the language of real closed fields by at least one new function or relation symbol, the L-theory of o-minimality is not recursively axiomatizable. In particular, for any recursive list of axioms A which is consistent with the L-theory of o-minimality, we find that there are locally o-minimal, definably complete structures satisfying A which are not elementarily equivalent to an ultraproduct of o-minimal structures. We call the latter sort of structures pseudo-o-minimal. In the second part we investigate uniform finiteness and cell decomposition in the pseudo-o-minimal setting. To do this, we introduce the notion of a pseudo-o-minimal structure tallying a discrete definable set. Investigating this notion, we answer some questions of uniqueness and existence. Finally, we show that under certain assumptions about the discrete definable sets that a given pseudo-o-minimal structure can tally, we have a version of uniform finiteness, at least in the planar case. This is the first step towards a cell decomposition theorem in this setting. In the final section, we look into two classes of examples of ultraproducts of o-minimal structures. For the first class, we note the o-minimality of a certain subset of these structures, and show the non-o-minimality of another. In particular, we derive the o-minimality of a new structure related to the real field with the exponential function. The second class is relatively intractable, but we discuss its relation to an important open problem in o-minimality.
Author | : Mário J. Edmundo |
Publisher | : Cuvillier Verlag |
Total Pages | : 223 |
Release | : 2005 |
Genre | : |
ISBN | : 386537557X |
Download O-minimal Structures Book in PDF, ePub and Kindle
Author | : Javier Esparza |
Publisher | : Cambridge University Press |
Total Pages | : 355 |
Release | : 2011-03-10 |
Genre | : Computers |
ISBN | : 0521718201 |
Download Finite and Algorithmic Model Theory Book in PDF, ePub and Kindle
Surveys of current research in logical aspects of computer science that apply finite and infinite model-theoretic methods.
Author | : Ya'acov Amos Peterzil |
Publisher | : |
Total Pages | : 190 |
Release | : 1991 |
Genre | : |
ISBN | : |
Download Some Definability Questions in Structures Over the Reals and in General O-minimal Structures Book in PDF, ePub and Kindle
Author | : Jan Van Eijck |
Publisher | : Cambridge University Press |
Total Pages | : |
Release | : 2017-03-30 |
Genre | : Mathematics |
ISBN | : 1108583482 |
Download Logic Colloquium '99 Book in PDF, ePub and Kindle
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the seventeenth publication in the Lecture Notes in Logic series, collects the proceedings of the European Summer Meeting of the Association for Symbolic Logic, held in Utrecht, The Netherlands in August, 1999. It includes surveys and research articles from some of the world's preeminent logicians. Two long articles are based on tutorials given at the meeting and present accessible expositions of current research in geometric model theory and the descriptive set theory of group actions. The other articles cover current research topics in all areas of mathematical logic, including proof theory, set theory, model theory, computability theory and philosophy.
Author | : Gil Keren |
Publisher | : |
Total Pages | : 58 |
Release | : 2014 |
Genre | : Compact groups |
ISBN | : |
Download Definable Compactness in Weakly O-minimal Structures Book in PDF, ePub and Kindle
Author | : Wilfrid Hodges |
Publisher | : Cambridge University Press |
Total Pages | : 322 |
Release | : 1997-04-10 |
Genre | : Mathematics |
ISBN | : 9780521587136 |
Download A Shorter Model Theory Book in PDF, ePub and Kindle
This is an up-to-date textbook of model theory taking the reader from first definitions to Morley's theorem and the elementary parts of stability theory. Besides standard results such as the compactness and omitting types theorems, it also describes various links with algebra, including the Skolem-Tarski method of quantifier elimination, model completeness, automorphism groups and omega-categoricity, ultraproducts, O-minimality and structures of finite Morley rank. The material on back-and-forth equivalences, interpretations and zero-one laws can serve as an introduction to applications of model theory in computer science. Each chapter finishes with a brief commentary on the literature and suggestions for further reading. This book will benefit graduate students with an interest in model theory.
Author | : Trent Harlan Ohl |
Publisher | : |
Total Pages | : 142 |
Release | : 2020 |
Genre | : First-order logic |
ISBN | : |
Download The First-order Theory of Expansions of O-minimal Structures by the Image of a Fast Sequence Book in PDF, ePub and Kindle
In "Expansions of o-minimal structures by fast sequences", H. Friedman and C. Miller introduced the notion of a fast sequence in o-minimal expansions of the real numbers; they studied the definability theory of expansions of o-minimal structures on the ordered additive group of real numbers by the image of a fast sequence, and they gave several characterizations of the definable sets [J. Symbolic Logic 70 (2005), no. 2, 410]. In such expansions, a fast sequence is an increasing, unbounded sequence such that the growth rate of the associated successor function exceeds the growth rate of any definable unary function restricted to the image of the sequence. This dissertation expands on the work of Friedman and Miller by examining the model theory of the expansion of an o-minimal structure on a linearly ordered group by the image of a fast sequence, including the issue of relative axiomatization. The completeness of the presented axioms follows from a quantifier elimination result for certain interdefinable structures, and the proof of the quantifier elimination result is an adaptation of methods that were used by C. Miller and J. Tyne in "Expansions of o-minimal structures by iteration sequences" [Notre Dame J. Formal Logic 47 (2006), no. 1, 93]. Several consequences of the relative axiomatization are inspired by related results of Friedman and Miller or of Miller and Tyne; for example, the boundary (with respect to the order topology) of every definable unary set of such expansions is a union of finitely many discrete sets. Other consequences include decidability and relative decidability results for specific examples of expansions of an o-minimal structure on a linearly ordered group by the image of a fast sequence.
Author | : Hans Schoutens |
Publisher | : Springer |
Total Pages | : 215 |
Release | : 2010-07-16 |
Genre | : Mathematics |
ISBN | : 3642133681 |
Download The Use of Ultraproducts in Commutative Algebra Book in PDF, ePub and Kindle
In spite of some recent applications of ultraproducts in algebra, they remain largely unknown to commutative algebraists, in part because they do not preserve basic properties such as Noetherianity. This work wants to make a strong case against these prejudices. More precisely, it studies ultraproducts of Noetherian local rings from a purely algebraic perspective, as well as how they can be used to transfer results between the positive and zero characteristics, to derive uniform bounds, to define tight closure in characteristic zero, and to prove asymptotic versions of homological conjectures in mixed characteristic. Some of these results are obtained using variants called chromatic products, which are often even Noetherian. This book, neither assuming nor using any logical formalism, is intended for algebraists and geometers, in the hope of popularizing ultraproducts and their applications in algebra.
Author | : Sirakov Boyan |
Publisher | : World Scientific |
Total Pages | : 5396 |
Release | : 2019-02-27 |
Genre | : Mathematics |
ISBN | : 9813272899 |
Download Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) Book in PDF, ePub and Kindle
The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.