Assume AD+V=L(R). In the first chapter, let W^1_1 denote the club measure on \omega_1. We analyze the embedding j_{W^1_1}\restr HOD from the point of view of inner model theory. We use our analysis to answer a question of Jackson-Ketchersid about codes for ordinals less than \omega_\omega. In the second chapter, we provide an indiscernibles analysis for models of the form L[T_n,x]. We use our analysis to provide new proofs of the strong partition property on \delta^1_{2n+1}

We extend previous work on classifying o-minimal types, and develop several applications. Marker developed a dichotomy of o-minimal types into "cuts" and "noncuts," with a further dichotomy of cuts being either "uniquely" or "non-uniquely realizable." We use this classification to extend work by van den Dries and Miller on bounding growth rates of definable functions in Chapter 3, and work by Marker on constructing certain "small" extensions in Chapter 4. We further sub-classify "non-uniquely realizable cuts" into three categories in Chapter 2, and we give define the notion of a "decreasing" type in Chapter 5, which is a presentation of a type well-suited for our work. Using this definition, we achieve two results: in Chapter 5.2, we improve a characterization of definable types in o-minimal theories given by Marker and Steinhorn, and in Chapter 6 we answer a question of Speissegger's about extending a continuous function to the boundary of its domain. As well, in Chapter 5.3, we show how every elementary extension can be presented as decreasing.

Thesis (Ph. D.)--York University, 1999. Graduate Programme in Mathematics and Statistics. / Typescript. Includes bibliographical references (leaves 87-93). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://wwwlib.umi.com/cr/yorku/fullcit?pNQ43427.

No description available.

Thesis (M.S.)--University of Texas at El Paso, 2008. / Title from title screen. Vita. CD-ROM. Includes bibliographical references. Also available online.

Let Zp be the ring of p-adic integers and Ep be the map x-->exp(px) where exp denotes the exponential map determined by the usual power series. It defines an exponential ring (Zp, + , . , 0, 1, Ep). The goal of the thesis is to study the model theory of this structure. In particular, we are interested by the question of the decidability of this theory. The main theorem of the thesis is: Theorem: If the p-adic Schanuel's conjecture is true, then the theory of (Zp, + , . , 0, 1, Ep) is decidable. The proof involves: 1- A result of effective model-completeness (chapters 3 and 4): If F is a family of restricted analytic functions (i.e. power series with coefficients in the valuation ring and convergent on Zp) closed under decomposition functions and such that the set of terms in the language LF= (+, . , 0, 1, f; f in F) is closed under derivation, then we prove that the theory of Zp in the language LF is model-complete. And furthermore, if each term of LF has an effective Weierstrass bound, then the model-completeness is effective. 2- A resolution of the decision problem for existential formulas (assuming Schanuel's conjecture) in chapter 5. We also consider the problem of the decidability of the structure (Op, + , . , 0, 1, |, E_p) where Op denotes the valuation ring of Cp. We give a positive answer to this question assuming the p-adic Schanuel's conjecture.

No description available.

No description available.

Model theory can express properties of algebraic subsets of complex n-space. The constructible subsets are precisely the first order definable subsets, and varieties correspond to maximal consistent collections of formulas, called types. Moreover, the topological dimension of a constructible set is equal to the Morley rank of the formula which defines it.

No description available.