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

Thesis (Ph. D.)--University of Wisconsin--Madison, 1982. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 148-150).

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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.

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This thesis explores some of the relationships between model theoretic and algebraic properties of fields, focusing on valuations of fields. We first show that the dp-rank of henselian valued fields admitting relative quantifier elimination is equal to the sum of the dp-ranks of the value group and of the residue field. Moreover, we give a characterization of henselianity of valued fields of finite dp-rank in terms of the dp-rank of definable sets. We also obtain partial results generalizing the work of Johnson in classifying fields of finite dp-rank. Finally, we consider fields with the property that the algebraic closure is an immediate extension with respect to every valuation. We show that under certain conditions these fields are dense in their algebraic closure with respect to every valuation and provide an example that demonstrates that this property does not hold in general. / Thesis / Doctor of Philosophy (PhD)

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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.

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Thesis advisor: Sara Moorman / This research looks at the ways in which mothers influence their daughter’s educational achievements and occupational aspirations. The goal is to determine whether the Role-Model Hypothesis or Grades Hypothesis explains the relationship more. According to the literature, the Role-Model Hypothesis is based on ideas of socialization and gender-role stereotypes while the Grades Hypothesis is based on the idea of transmission of social capital, which improves test scores. In order to test these hypotheses, a series of multinomial logistic regression models were run on the responses of a sample of 7,716 female students and their mothers to the Educational Longitudinal Study, (ELS) 2002, Base Year. The results provide evidence in support of the Grades Hypothesis. A mother with higher educational attainment and a more prestigious occupation is more likely to have a daughter with higher test scores, with higher test scores leading to higher expectations and aspirations by the daughter. Implications of this finding include suggestions for the need for action, policy changes, and the decline in the importance of gender theory in influencing aspirations. / Thesis (BA) — Boston College, 2013. / Submitted to: Boston College. College of Arts and Sciences. / Discipline: College Honors Program. / Discipline: Sociology Honors Program. / Discipline: Sociology.