The theory of the exponential differential equations of semiabelian varieties

The complete first order theories of the exponential differential equations of semiabelian varieties are given. It is shown that these theories also arises from an amalgamation-with-predimension construction in the style of Hrushovski. The theory includes necessary and sufficient conditions for a system of equations to have a solution. The necessary condition generalizes Ax's differential fields version of Schanuel's conjecture to semiabelian varieties. There is a purely algebraic corollary, the "Weak CIT" for semiabelian varieties, which concerns the intersections of algebraic subgroups with algebraic varieties.Comment: 53 pages; v3: Substantial changes, including a completely new introductio

Vienna Circle and Logical Analysis of Relativity Theory

In this paper we present some of our school's results in the area of building up relativity theory (RT) as a hierarchy of theories in the sense of logic. We use plain first-order logic (FOL) as in the foundation of mathematics (FOM) and we build on experience gained in FOM. The main aims of our school are the following: We want to base the theory on simple, unambiguous axioms with clear meanings. It should be absolutely understandable for any reader what the axioms say and the reader can decide about each axiom whether he likes it. The theory should be built up from these axioms in a straightforward, logical manner. We want to provide an analysis of the logical structure of the theory. We investigate which axioms are needed for which predictions of RT. We want to make RT more transparent logically, easier to understand, easier to change, modular, and easier to teach. We want to obtain deeper understanding of RT. Our work can be considered as a case-study showing that the Vienna Circle's (VC) approach to doing science is workable and fruitful when performed with using the insights and tools of mathematical logic acquired since its formation years at the very time of the VC activity. We think that logical positivism was based on the insight and anticipation of what mathematical logic is capable when elaborated to some depth. Logical positivism, in great part represented by VC, influenced and took part in the birth of modern mathematical logic. The members of VC were brave forerunners and pioneers.Comment: 25 pages, 1 firgure

Perceptions about the elisa test of people diagnosed at the aids stage

Indexación: Web of Science; Scopus; Scielo.Background: The delay in the diagnosis of AIDS results in higher treatment costs. Aim: To reveal the experiences of people who were diagnosed in the AIDS stage about the access to the ELISA test. Material and Methods: In depth interviews were carried out to 15 participants from public hospitals who were in the AIDS stage at the moment of the diagnosis. The main questions asked were about the motivations to take the test, the barriers found and the help received from the health care personnel. All interviews were recorded and analyzed according to Kripperdorff. Results: The three categories that emerged were the motivations to take the test, the facilitators found and the difficulties to access to the test. The main motivation was a condition of vulnerability due to the suspicion or certainty of being infected. The main facilitator was the sensation of being accepted and not discriminated. The main difficulties were the fear of having a positive test and of being discriminated and the lack of information. Conclusions: Knowing these experiences will help to improve the early detection of HIV infections.http://ref.scielo.org/m53w8

Conservative and disruptive modes of adolescent change in human brain functional connectivity

Adolescent changes in human brain function are not entirely understood. Here, we used multiecho functional MRI (fMRI) to measure developmental change in functional connectivity (FC) of resting-state oscillations between pairs of 330 cortical regions and 16 subcortical regions in 298 healthy adolescents scanned 520 times. Participants were aged 14 to 26 y and were scanned on 1 to 3 occasions at least 6 mo apart. We found 2 distinct modes of age-related change in FC: “conservative” and “disruptive.” Conservative development was characteristic of primary cortex, which was strongly connected at 14 y and became even more connected in the period from 14 to 26 y. Disruptive development was characteristic of association cortex and subcortical regions, where connectivity was remodeled: connections that were weak at 14 y became stronger during adolescence, and connections that were strong at 14 y became weaker. These modes of development were quantified using the maturational index (MI), estimated as Spearman’s correlation between edgewise baseline FC (at 14 y, FC14) and adolescent change in FC (ΔFC14−26), at each region. Disruptive systems (with negative MI) were activated by social cognition and autobiographical memory tasks in prior fMRI data and significantly colocated with prior maps of aerobic glycolysis (AG), AG-related gene expression, postnatal cortical surface expansion, and adolescent shrinkage of cortical thickness. The presence of these 2 modes of development was robust to numerous sensitivity analyses. We conclude that human brain organization is disrupted during adolescence by remodeling of FC between association cortical and subcortical areas

Expansive actions on uniform spaces and surjunctive maps

We present a uniform version of a result of M. Gromov on the surjunctivity of maps commuting with expansive group actions and discuss several applications. We prove in particular that for any group $\Gamma$ and any field \K, the space of $\Gamma$-marked groups $G$ such that the group algebra \K[G] is stably finite is compact.Comment: 21 page

Comparing theories: the dynamics of changing vocabulary. A case-study in relativity theory

There are several first-order logic (FOL) axiomatizations of special relativity theory in the literature, all looking essentially different but claiming to axiomatize the same physical theory. In this paper, we elaborate a comparison, in the framework of mathematical logic, between these FOL theories for special relativity. For this comparison, we use a version of mathematical definability theory in which new entities can also be defined besides new relations over already available entities. In particular, we build an interpretation of the reference-frame oriented theory SpecRel into the observationally oriented Signalling theory of James Ax. This interpretation provides SpecRel with an operational/experimental semantics. Then we make precise, "quantitative" comparisons between these two theories via using the notion of definitional equivalence. This is an application of logic to the philosophy of science and physics in the spirit of Johan van Benthem's work.Comment: 27 pages, 8 figures. To appear in Springer Book series Trends in Logi

Twin Paradox and the logical foundation of relativity theory

We study the foundation of space-time theory in the framework of first-order logic (FOL). Since the foundation of mathematics has been successfully carried through (via set theory) in FOL, it is not entirely impossible to do the same for space-time theory (or relativity). First we recall a simple and streamlined FOL-axiomatization SpecRel of special relativity from the literature. SpecRel is complete with respect to questions about inertial motion. Then we ask ourselves whether we can prove usual relativistic properties of accelerated motion (e.g., clocks in acceleration) in SpecRel. As it turns out, this is practically equivalent to asking whether SpecRel is strong enough to "handle" (or treat) accelerated observers. We show that there is a mathematical principle called induction (IND) coming from real analysis which needs to be added to SpecRel in order to handle situations involving relativistic acceleration. We present an extended version AccRel of SpecRel which is strong enough to handle accelerated motion, in particular, accelerated observers. Among others, we show that the Twin Paradox becomes provable in AccRel, but it is not provable without IND.Comment: 24 pages, 6 figure