In [16], Peterzil and Steinhorn proved that if a group G definable in an o-minimal structure is not definably compact, then G contains a definable torsion-free subgroup of dimension 1. We prove here a p-adic analogue of the Peterzil–Steinhorn theorem, in the special case of abelian groups. Let G be an abelian group definable in a p-adically closed field M. If G is not definably compact then there is a definable subgroup H of dimension 1 which is not definably compact. (...) In a future paper we will generalize this to non-abelian G. (shrink)

We construct a nontrivial definable type V field topology on any dp-minimal field K that is not strongly minimal, and prove that definable subsets of Kn have small boundary. Using this topology and...

Recall that a group G has finitely satisfiable generics (fsg) or definable f-generics (dfg) if there is a global type p on G and a small model $M_0$ such that every left translate of p is finitely satisfiable in $M_0$ or definable over $M_0$, respectively. We show that any abelian group definable in a p-adically closed field is an extension of a definably compact fsg definable group by a dfg definable group. We discuss an approach which might prove a similar (...) statement for interpretable abelian groups. In the case where G is an abelian group definable in the standard model $\mathbb {Q}_p$, we show that $G^0 = G^{00}$, and that G is an open subgroup of an algebraic group, up to finite factors. This latter result can be seen as a rough classification of abelian definable groups in $\mathbb {Q}_p$. (shrink)

Let G be a definable group in a p-adically closed field M. We show that G has finitely satisfiable generics ( fsg $\text{fsg}$ ) if and only if G is definably compact. The case M = Q p $M = \mathbb {Q}_p$ was previously proved by Onshuus and Pillay.

We give a simplified proof of elimination of imaginaries in ACVF, based on ideas of Hrushovski. This proof manages to avoid many of the technical issues which arose in the original proof by Haskell, Hrushovski, and Macpherson.

We consider interpretable topological spaces and topological groups in a p-adically closed field K. We identify a special class of “admissible topologies” with topological tameness properties like generic continuity, similar to the topology on definable subsets of Kn. We show that every interpretable set has at least one admissible topology, and that every interpretable group has a unique admissible group topology. We then consider definable compactness (in the sense of Fornasiero) on interpretable groups. We show that an interpretable group is (...) definably compact if and only if it has finitely satisfiable generics (fsg), generalizing an earlier result on definable groups. As a consequence, we see that fsg is a definable property in definable families of interpretable groups, and that any fsg interpretable group defined over Qp is definably isomorphic to a definable group. (shrink)

We prove that NIP valued fields of positive characteristic are henselian, and we begin to generalize the known results on dp-minimal fields to dp-finite fields. On any unstable dp-finite field K, we define a type-definable group of “infinitesimals,” corresponding to a canonical group topology on (K, +). We reduce the classification of positive characteristic dp-finite fields to the construction of non-trivial Aut(K/A)-invariant valuation rings.

We consider existentially closed fields with several orderings, valuations, and [Formula: see text]-valuations. We show that these structures are NTP2 of finite burden, but usually have the independence property. Moreover, forking agrees with dividing, and forking can be characterized in terms of forking in ACVF, RCF, and [Formula: see text]CF.

We consider existentially closed fields with several orderings, valuations, and p-valuations. We show that these structures are NTP2 of finite burden, but usually have the independence property. Mo...

We generalize two of our previous results on abelian definable groups in p-adically closed fields [12, 13] to the non-abelian case. First, we show that if G is a definable group that is not definably compact, then G has a one-dimensional definable subgroup which is not definably compact. This is a p-adic analogue of the Peterzil–Steinhorn theorem for o-minimal theories [16]. Second, we show that if G is a group definable over the standard model $\mathbb {Q}_p$, then $G^0 = G^{00}$. (...) As an application, definably amenable groups over $\mathbb {Q}_p$ are open subgroups of algebraic groups, up to finite factors. We also prove that $G^0 = G^{00}$ when G is a definable subgroup of a linear algebraic group, over any model. (shrink)

Let T be a theory. If T eliminates \, it need not follow that \ eliminates \, as shown by the example of the p-adics. We give a criterion to determine whether \ eliminates \. Specifically, we show that \ eliminates \ if and only if \ is eliminated on all interpretable sets of “unary imaginaries.” This criterion can be applied in cases where a full description of \ is unknown. As an application, we show that \ eliminates \ when (...) T is a C-minimal expansion of ACVF. (shrink)

Historically, deserts have served to distinguish the essential from the superfluous. Therefore, a desert experience has been an excellent lens with which to focus on what really matters and to learn what may be impossible to learn in more stable environments. The desert experience of the ancient Hebrews, as they journeyed from Egypt, land of slavery, to Canaan, land of promise, embodied a number of timeless spiritual truths in the context of an environmental framework where priorities became crystal clear. Three (...) elements of this framework will be presented here as we examine the Jewish people, liberated in a land "that was not sown." First, the desert environment revealed the reality of God. While the portrait of God painted on the sandy canvas of the Sinai Peninsula was incomplete, it served well to reacquaint this wayward people with their Lord. Second, the way in which the Israelites were sustained pictures a specific attribute of God, that of provider. He actively met the needs of His chosen people as a loving father meets the needs of his children. God provided everything from food and water for physical survival to discipline and guidance for healthy spiritual and emotional growth. Finally, their desert experience illustrated that disobeying God caused environmental disaster. The desert they crossed sustained life when the Israelites trusted God but failed to do so when they disobeyed Him. Through the physical experience of wandering in the wilderness, the Hebrews learned a spiritual lesson of faith and saw how their corporate faith affected the quality of the natural environment for the entire nation. This timeless lesson, if applied today would result in significant environmental improvement worldwide. Moreover, brethren, I would not that ye should be ignorant, how that all our fathers were under the cloud, and all passed through the sea; And were all baptized unto Moses in the cloud and in the sea; And did all eat the same spiritual meat; And did all drink the same spiritual drink: for they drank of that spiritual Rock that followed them: and that Rock was Christ. But with many of them God was not well pleased: for they were overthrown in the wilderness. Now all these things happened unto them for ensamples: and they are written for our admonition, upon whom the ends of the world are come. Wherefore let him that thinketh he standeth take heed lest he fall. There hath no temptation taken you but such as is common to man: but God is faithful, who will not suffer you to be tempted above that ye are able; but will with the temptation also make a way to escape, that ye may be able to bear it. I Corinthians 10:1-5,11-13. (shrink)

A new intellectual climate is emerging for rethinking the God of revelation who is unreservedly for and with human beings and who, in turn, calls us to be for and with the Other.

This article's thesis is that religion and science are ultimately about the same thing, that they affect one another, and that people in the two fields therefore need to communicate. The authors begin by discussing the importance of ethical transformations to a life of love and character, arguing that the development of a technological society does not free us from ethical demands. They then move to advocating dialogue about the shared truths of science and religion. Wanting both, and positing that (...) the former is a foundation for the latter, the authors state that Einstein's famous logian cannot be ignored: "The situation may be expressed by an image: Science without religion is lame, religion without science is blind". (shrink)

The genetic interaction between mother and fetus during pregnancy is discussed, focusing on teratogenic alleles that act in the mother to alter fetal development and contribute to a neurodevelopmental disorder. For these alleles, the mother is the genetic patient. Teratogenic alleles interact with modifying and specificity alleles that act in the fetus and with environmental factors. Based on examples of the model, two candidate mechanisms emerge as contributors to neurodevelopmental disorders, folate‐homocysteine pathways and immune/inflammatory mechanisms. Both, acting in mothers, affect (...) fetal development and contain many polymorphic genes. These two systems interact with each other. Common functional polymorphisms of mild effect in these two systems of interacting genes are good candidates for teratogenic alleles. The presence of teratogenic alleles complicates gene identification for neurodevelopmental disorders. However, using the special methods required to identify teratogenic alleles is important because this could lead to new approaches to prevention and improved therapy of these disorders. BioEssays 25:464–477, 2003. © 2003 Wiley Periodicals, Inc. (shrink)

It may come as a surprise to some, but the Bible has a great deal to say about the environment and its conservation some 20 centuries since it was written. Perhaps among the most surprised will be Bible-toting church goers who may have never heard a sermon related to the "environmental crisis" which has become such a concern to so many around the world. This lack of attention by Christians is especially perplexing since many of our environmental problems are rooted (...) in the Christian faith, according to some scholars. However, by examining the doctrine of Christianity, the basic text of the faith, the Bible, we find an entirely different message. The purpose of this discussion is to present the entire portion of Scripture which relates to environmental principles whereby we may develop a Bible-based, 21st Century prescription of environmental conservation. Some 2,463 verses have been topically organized into nine sections. Four appendices present the full-text of this collection in addition to selected hymns, which have been instrumental in teaching the truths of Scripture over the years. This compilation of verses constitutes approximately eight percent of the Bible. The Authorized Version, also known as the King James Version, was used in the preparation of this collection due its widespread distribution and influence since 1611. Based on the Bible, Christianity’s positive contribution to environmental conservation is consistent with its positive contributions to other fields such as literature, art, music, education, health, and science. (shrink)

We examine initial public offering (IPO) holdings in the mutual funds of four large investment banks and five large non-investment banks during the period 1997 through 2002. Investment banks hold IPOs with different characteristics than IPOs held by noninvestment banks, and they also tend to hold IPOs in different types of funds than non-investment banks. We classify holdings as to whether the IPO lies outside or inside the fund's objective. Investment banks hold IPOs outside the fund objective in 27% of (...) the fund/IPO pairs while non-investment banks hold outside their objective in just 5.4% of fund/IPO pairs. We see significant differences in IPO underpricing for both groups as well. For example, when non-investment banks hold IPOs outside a large capitalization fund objective, they select IPOs with 52% higher underpricing as measured by first-day returns. (shrink)

The study of the Second Sophistic is a relative newcomer to the Anglophone field of classics, and much of what characterizes it temporally and culturally remains a matter of legitimate contestation. This Handbook offers a diversity of scholarly voices that attempt to define the state of this developing field. Included are chapters that offer practical guidance on the wide range of valuable textual materials that survive, many of which are useful or even core to inquiries of particularly current interest (e.g., (...) gender studies, cultural history of the body, sociology of literary culture, history of education and intellectualism, history of religion, political theory, history of medicine, cultural linguistics, intersection of the classical traditions and early Christianity). (shrink)

"The search for transcendence is an absorbing and ongoing enterprise. Transcendence is the most discussed, the most compelling, and the most engaging of the subjects with which contemporary theologians deal ... The impulse to move from the ordinary dimensions of life to the extraordinary is not invented by the theologians but is one which appears to spring up from the deepest levels of consciousness itself." [Introduction].