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University of Illinois – Urbana-Champaign

1. Gehret, Allen R. Towards a model theory of logarithmic transseries.

Degree: PhD, Mathematics, 2017, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/98343

► The ordered valued differential field \mathbb{T}_{log} of logarithmic transseries is conjectured to have good model theoretic properties. This thesis records our progress in this direction…
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Subjects/Keywords: Logarithmic transseries; Model theory

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Gehret, A. R. (2017). Towards a model theory of logarithmic transseries. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/98343

Chicago Manual of Style (16^{th} Edition):

Gehret, Allen R. “Towards a model theory of logarithmic transseries.” 2017. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 20, 2019. http://hdl.handle.net/2142/98343.

MLA Handbook (7^{th} Edition):

Gehret, Allen R. “Towards a model theory of logarithmic transseries.” 2017. Web. 20 Jul 2019.

Vancouver:

Gehret AR. Towards a model theory of logarithmic transseries. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2017. [cited 2019 Jul 20]. Available from: http://hdl.handle.net/2142/98343.

Council of Science Editors:

Gehret AR. Towards a model theory of logarithmic transseries. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2017. Available from: http://hdl.handle.net/2142/98343

University of Illinois – Urbana-Champaign

2. Camacho Ahumada, Santiago. Truncation in differential Hahn fields.

Degree: PhD, Mathematics, 2018, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/100890

► Being closed under truncation for subsets of generalized series fields is a robust property in the sense that it is preserved under various algebraic and…
(more)

Subjects/Keywords: Valued Fields; Transseries; Truncation; Differential Algebra; Hahn Fields

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APA (6^{th} Edition):

Camacho Ahumada, S. (2018). Truncation in differential Hahn fields. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/100890

Chicago Manual of Style (16^{th} Edition):

Camacho Ahumada, Santiago. “Truncation in differential Hahn fields.” 2018. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 20, 2019. http://hdl.handle.net/2142/100890.

MLA Handbook (7^{th} Edition):

Camacho Ahumada, Santiago. “Truncation in differential Hahn fields.” 2018. Web. 20 Jul 2019.

Vancouver:

Camacho Ahumada S. Truncation in differential Hahn fields. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2018. [cited 2019 Jul 20]. Available from: http://hdl.handle.net/2142/100890.

Council of Science Editors:

Camacho Ahumada S. Truncation in differential Hahn fields. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2018. Available from: http://hdl.handle.net/2142/100890

University of Illinois – Urbana-Champaign

3. Tellez, Hernando. Contributions to model theory of metric structures.

Degree: PhD, 0439, 2010, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/16109

► Two Banach spaces X and Y are said to be almost isometric if for every ?? > 1 there exists a ??-isomorphism f : X…
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Subjects/Keywords: Continuous logic; Metric structures; Model theory; Perturbations; Banach spaces; Algebraic closure

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APA (6^{th} Edition):

Tellez, H. (2010). Contributions to model theory of metric structures. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/16109

Chicago Manual of Style (16^{th} Edition):

Tellez, Hernando. “Contributions to model theory of metric structures.” 2010. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 20, 2019. http://hdl.handle.net/2142/16109.

MLA Handbook (7^{th} Edition):

Tellez, Hernando. “Contributions to model theory of metric structures.” 2010. Web. 20 Jul 2019.

Vancouver:

Tellez H. Contributions to model theory of metric structures. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2010. [cited 2019 Jul 20]. Available from: http://hdl.handle.net/2142/16109.

Council of Science Editors:

Tellez H. Contributions to model theory of metric structures. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2010. Available from: http://hdl.handle.net/2142/16109

University of Illinois – Urbana-Champaign

4. Song, Shichang. Model theory and probability.

Degree: PhD, 0439, 2012, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/29825

► This thesis presents a systematic study of the model theory of probability algebras, random variable structures, and adapted structures, with an emphasis on their atomless…
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Subjects/Keywords: Model theory; continuous logic; probability algebras; random variables; adapted spaces

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APA (6^{th} Edition):

Song, S. (2012). Model theory and probability. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/29825

Chicago Manual of Style (16^{th} Edition):

Song, Shichang. “Model theory and probability.” 2012. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 20, 2019. http://hdl.handle.net/2142/29825.

MLA Handbook (7^{th} Edition):

Song, Shichang. “Model theory and probability.” 2012. Web. 20 Jul 2019.

Vancouver:

Song S. Model theory and probability. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2012. [cited 2019 Jul 20]. Available from: http://hdl.handle.net/2142/29825.

Council of Science Editors:

Song S. Model theory and probability. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2012. Available from: http://hdl.handle.net/2142/29825

5. Caulfield, Erin. Classifying expansions of the real field by complex subgroups.

Degree: PhD, Mathematics, 2018, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/101541

► In this thesis, we study expansions of the real field by multiplicative subgroups of the complex numbers. We first consider expansions by a subgroup generated…
(more)

Subjects/Keywords: Expansions of the real field; Complex subgroups; Model theory

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APA (6^{th} Edition):

Caulfield, E. (2018). Classifying expansions of the real field by complex subgroups. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/101541

Chicago Manual of Style (16^{th} Edition):

Caulfield, Erin. “Classifying expansions of the real field by complex subgroups.” 2018. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 20, 2019. http://hdl.handle.net/2142/101541.

MLA Handbook (7^{th} Edition):

Caulfield, Erin. “Classifying expansions of the real field by complex subgroups.” 2018. Web. 20 Jul 2019.

Vancouver:

Caulfield E. Classifying expansions of the real field by complex subgroups. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2018. [cited 2019 Jul 20]. Available from: http://hdl.handle.net/2142/101541.

Council of Science Editors:

Caulfield E. Classifying expansions of the real field by complex subgroups. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2018. Available from: http://hdl.handle.net/2142/101541

6. Hakobyan, Tigran. Algebraically closed fields with characters; differential-henselian monotone valued differential fields.

Degree: PhD, Mathematics, 2018, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/101483

► This thesis consists of two unrelated research projects. In the first project we study the model theory of the 2-sorted structure (F, C; χ), where…
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Subjects/Keywords: mathematical logic; model theory; quantifier elimination; NIP; fields; algebraically closed fields; characters; differential fields; valued fields; valued differential fields; d-henselian fields; monotone valued differential fields; Ax-Kochen-Ershov principle; Ax-Kochen principle

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Hakobyan, T. (2018). Algebraically closed fields with characters; differential-henselian monotone valued differential fields. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/101483

Chicago Manual of Style (16^{th} Edition):

Hakobyan, Tigran. “Algebraically closed fields with characters; differential-henselian monotone valued differential fields.” 2018. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 20, 2019. http://hdl.handle.net/2142/101483.

MLA Handbook (7^{th} Edition):

Hakobyan, Tigran. “Algebraically closed fields with characters; differential-henselian monotone valued differential fields.” 2018. Web. 20 Jul 2019.

Vancouver:

Hakobyan T. Algebraically closed fields with characters; differential-henselian monotone valued differential fields. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2018. [cited 2019 Jul 20]. Available from: http://hdl.handle.net/2142/101483.

Council of Science Editors:

Hakobyan T. Algebraically closed fields with characters; differential-henselian monotone valued differential fields. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2018. Available from: http://hdl.handle.net/2142/101483

7. Panagiotopoulos, Aristotelis. Structures and dynamics.

Degree: PhD, Mathematics, 2017, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/98378

► Our results are divided in three independent chapters. In Chapter 2, we show that if g is a generic isometry of a generic subspace X…
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Subjects/Keywords: Polish groups; Fraisse; Turbulence; Hjorth; Left invariant; Becker; Projective Fraisse; Infinite games; Borel complexity

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Panagiotopoulos, A. (2017). Structures and dynamics. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/98378

Chicago Manual of Style (16^{th} Edition):

Panagiotopoulos, Aristotelis. “Structures and dynamics.” 2017. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 20, 2019. http://hdl.handle.net/2142/98378.

MLA Handbook (7^{th} Edition):

Panagiotopoulos, Aristotelis. “Structures and dynamics.” 2017. Web. 20 Jul 2019.

Vancouver:

Panagiotopoulos A. Structures and dynamics. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2017. [cited 2019 Jul 20]. Available from: http://hdl.handle.net/2142/98378.

Council of Science Editors:

Panagiotopoulos A. Structures and dynamics. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2017. Available from: http://hdl.handle.net/2142/98378

8. Kwiatkowska, Aleksandra. Dynamics of Polish groups.

Degree: PhD, 0439, 2012, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/34394

► This thesis consists of an introduction and two independent chapters. In Chapter 2, we show that the group of all homeomorphisms of the Cantor set…
(more)

Subjects/Keywords: Polish groups; ample generics; Boolean actions; isometry groups

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APA (6^{th} Edition):

Kwiatkowska, A. (2012). Dynamics of Polish groups. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/34394

Chicago Manual of Style (16^{th} Edition):

Kwiatkowska, Aleksandra. “Dynamics of Polish groups.” 2012. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 20, 2019. http://hdl.handle.net/2142/34394.

MLA Handbook (7^{th} Edition):

Kwiatkowska, Aleksandra. “Dynamics of Polish groups.” 2012. Web. 20 Jul 2019.

Vancouver:

Kwiatkowska A. Dynamics of Polish groups. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2012. [cited 2019 Jul 20]. Available from: http://hdl.handle.net/2142/34394.

Council of Science Editors:

Kwiatkowska A. Dynamics of Polish groups. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2012. Available from: http://hdl.handle.net/2142/34394

9. Slutskyy, Kostyantyn. Extending partial isomorphisms.

Degree: PhD, 0439, 2012, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/30971

► There are two main topics in the thesis. In the second chapter we study two-dimensional classes of topological similarity in the groups of automorphisms of…
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Subjects/Keywords: Polish groups; Graev metrics; topological similarity; induced conjugacy classes; Urysohn space

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APA (6^{th} Edition):

Slutskyy, K. (2012). Extending partial isomorphisms. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/30971

Chicago Manual of Style (16^{th} Edition):

Slutskyy, Kostyantyn. “Extending partial isomorphisms.” 2012. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 20, 2019. http://hdl.handle.net/2142/30971.

MLA Handbook (7^{th} Edition):

Slutskyy, Kostyantyn. “Extending partial isomorphisms.” 2012. Web. 20 Jul 2019.

Vancouver:

Slutskyy K. Extending partial isomorphisms. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2012. [cited 2019 Jul 20]. Available from: http://hdl.handle.net/2142/30971.

Council of Science Editors:

Slutskyy K. Extending partial isomorphisms. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2012. Available from: http://hdl.handle.net/2142/30971

10. Hill, Aaron. Centralizers in automorphism groups.

Degree: PhD, 0439, 2011, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/26363

► In this dissertation we investigate centralizers in several automorphism groups of homogenous structures. In the rst chapter, we discuss the centralizer question in ergodic theory,…
(more)

Subjects/Keywords: Rank-1; Topological Complexity; Centralizer

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Hill, A. (2011). Centralizers in automorphism groups. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/26363

Chicago Manual of Style (16^{th} Edition):

Hill, Aaron. “Centralizers in automorphism groups.” 2011. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 20, 2019. http://hdl.handle.net/2142/26363.

MLA Handbook (7^{th} Edition):

Hill, Aaron. “Centralizers in automorphism groups.” 2011. Web. 20 Jul 2019.

Vancouver:

Hill A. Centralizers in automorphism groups. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2011. [cited 2019 Jul 20]. Available from: http://hdl.handle.net/2142/26363.

Council of Science Editors:

Hill A. Centralizers in automorphism groups. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2011. Available from: http://hdl.handle.net/2142/26363

11. Zhao, Min. Ramsey theory and its application.

Degree: PhD, 0439, 2015, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/72752

► In this dissertation, we study three problems about Ramsey theory. First, we prove a self-dual Ramsey theorem for parameter systems which is a generalization of…
(more)

Subjects/Keywords: Ramsey theory; abstract Ramsey theorem; Parameter system; Self-Dual; Partial order; Linear order; Interpretation

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Zhao, M. (2015). Ramsey theory and its application. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/72752

Chicago Manual of Style (16^{th} Edition):

Zhao, Min. “Ramsey theory and its application.” 2015. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed July 20, 2019. http://hdl.handle.net/2142/72752.

MLA Handbook (7^{th} Edition):

Zhao, Min. “Ramsey theory and its application.” 2015. Web. 20 Jul 2019.

Vancouver:

Zhao M. Ramsey theory and its application. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2015. [cited 2019 Jul 20]. Available from: http://hdl.handle.net/2142/72752.

Council of Science Editors:

Zhao M. Ramsey theory and its application. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2015. Available from: http://hdl.handle.net/2142/72752