Internal approach to external sets and universes

A problem which enthusiasts ofIST, Nelson's internal set theory, usually face is how to treat external sets in the internal universe which does not contain them directly. To solve this problem, we considerBST,bounded set theory, a modification ofIST which is, briefly, a theory for the family of thoseIST sets which are members of standard sets.We show thatBST is strong enough to incorporate external sets in the internal universe in a way sufficient to develop the most advanced applications of nonstandard methods. In particular, we define inBST an enlargement of theBST universe which satisfies the axioms ofHST, an external theory close to a theory introduced by Hrbaek. HST includes Replacement and Saturation for all formulas but contradicts the Power Set and Choice axioms (either of them is incompatible with Replacement plus Saturation), therefore to get an external universe which satisfies all ofZFC minus Regularity one has to pay by a restriction of Saturation. We prove thatHST admits a system of subuniverses which modelZFC (minus Regularity but with Power Set and Choice) and Saturation in a form restricted by a fixed but arbitrary standard cardinal.Thus the proposed system of set theoretic foundations for nonstandard mathematics, based on the simple and natural axioms of the internal theoryBST, provides the treatment of external sets sufficient to carry out elaborate external constructions.Partially supported by AMS grants in 1993 and 1994 and DFG grant in 1994.Presented byRobert Goldblatt     

Internal approach to external sets and universes

In this article we show how the universe ofBST,bounded set theory (a modification ofIST which is, briefly, a theory for the family of those sets inIST which are members of standard sets) can be enlarged by definable subclasses of sets (which are not necessarily sest in internal theories likeBST orIST) so that Separation and Replacement are true in the enlargement for all formulas, including those in which the standardness predicate may occur.ThusBST is strong enough to incorporate external sets in the internal universe in a way sufficient to develop topics in nonstandard analysis inaccessible in the framework of a purely internal approach, such as Loeb measures.Presented byRobert Goldblatt     

Internal approach to external sets and universes

In this article we show how the universe of HST, Hrbaek set theory (a nonstandard set theory of external type, which includes, in particular, the ZFC Replacement and Separation schemata for all formulas in the language containing the membership and standardness predicates, and Saturation for standard size families of internal sets, but does not include the Power set axiom) admits a system of subuniverses which keep the Replacement, model Power set and Choice (in fact all of ZFC, with the exception of the Regularity axiom, which indeed is replaced by the Regularity over the internal subuniverse), and also keep as much of Saturation as it is necessary.This gives sufficient tools to develop the most complicated topics in nonstandard analysis, such as Loeb measures.Partially supported by AMS grants in 1993 – 1995 and DFG grants in 1994 – 1995. Robert Goldblatt     

Internal and external motivation to respond without sexism

Based on Plant and Devine's (1998) measures of Internal and External Motivation to Respond Without Prejudice toward Blacks, new scales were developed to assess Internal and External Motivation to Respond Without Sexism (IMS-S and EMS-S, respectively). The scales possess good psychometric properties. Providing evidence of convergent and discriminant validity, the IMS-S was strongly related to measures of sexism yet unrelated to measures of social evaluation. The EMS-S was modestly related to both sexism and social evaluative concerns. Providing evidence of predictive validity, participants who were either internally or externally motivated to respond without sexism rated sexist jokes more negatively in a situation discouraging sexism compared to participants low in both sources of motivation. However, only high IMS-S participants rated the jokes negatively whether the situation encouraged or discouraged sexism and whether their response was public or private. Implications for understanding the similarities and differences between sexism and racism are discussed.     

Correlates of coping behaviours: Internal and external resources

This study examined some possible factors that were expected to influence choices of coping strategies. They were demographic variables (age, sex, marital status, education, and family income), personality traits (extroversion, neuroticism and locus of control), perceived life stress, and received social support. Five hundred and eighty one randomly selected community adults living in Kaohsiung city were interviewed and completed questionnaires measuring the above variables. Multivariate analyses had shown that: (a) higher income and education were related to more use of ‘Seeking social resources’ and ‘Planning & hoping’ coping; (b) higher extroversion was related to more use of ‘Seeking social resources’, ‘Planning & hoping’ and ‘Emotional suppression’ coping, whereas the last was also related to higher neuroticism; (c) people with higher internal locus of control favoured ‘Planning & hoping’, but not ‘Emotional suppression’ coping; (d) perceived life stress was not related to any use of coping behaviours; however, (e) more social support was related to more use of all kinds of coping behaviours. Implications of results were discussed in the context of stress and adaptation.     

Internal and external factors modulate food-calling in domestic hens

Two series of experiments investigated factors affecting utterance of food calls in the domestic hen, Gallus domesticus. The first series of experiments tested the effect of food preference and the hen’s internal state on the utterance of food calls. Different food types were presented first singly and then in a choice test to 20 hens, first when hens were laying, and then when they were maternal. The second series of experiments tested the effect of hunger level on the utterance of food calls in laying hens, and maternal hens with or without chicks. These two series of experiments showed that laying hens and maternal hens showed a similar marked preference for certain types of food, but laying hens very rarely emitted food calls, in contrast to maternal hens. This shows the effect of the bird’s psychophysiological state on her tendency to emit food calls. The more a maternal hen preferred a food type, the more food calls she emitted. This was observed from the beginning of a test in single-food tests as well as in choice tests. Hunger level positively affected food-call production under certain feeding conditions in maternal hens, but not in laying hens. When maternal hens were tested in the absence of their chicks, utterance of food calls was more sustained than in the presence of chicks. Received: 14 May 1998 / Accepted after revision: 11 October 1998     

Event-related potentials indicate that reality monitoring differs from external source monitoring

This experiment investigated differences in event-related potentials (ERPs) observed in 2 types of source monitoring decisions. Participants discriminated between self-generated, heard, and new words (reality monitoring) in one condition; in another they discriminated between words heard in a male or female voice and new items (external source monitoring). The data support the source monitoring framework, which argues that reality monitoring discriminations differ from external source monitoring discriminations. Analysis revealed better overall source accuracy during reality monitoring than during external source monitoring. In the external source monitoring task, an early old-new ERP difference was observed at parietal electrodes followed by frontal old-new effect that persisted longer, replicating previous ERP results. However, early ERP amplitude differences between sources were observed at parietal electrode sites during reality monitoring, suggesting that self-generated items activate more differentiated information during remembering. Furthermore, there were no frontal old-new ERP differences during reality monitoring, suggesting that different decision processes are used in these types of source monitoring decisions.     

Effects of an external focus of attention and target occlusion on performance in virtual reality

The use of virtual reality as a training mechanism continues to gain popularity as equipment becomes more readily available. It is important to not only understand the relationship between virtual reality training and motor learning, but to understand the extent to which practice manipulations enhance performance in virtual reality. One common practice manipulation is adopting an external focus of attention, which has been shown to facilitate motor learning in a variety tasks. The purposes of the present study were to investigate the effectiveness of an external focus of attention and the effects of target occlusion times in virtual reality. Fifty-six participants performed a single-leg long jump during baseline, training, and retention and were randomly assigned to either an external or control group. During baseline and retention, all participants performed the task in both a virtual reality (VR) and real world (RW) environments. Training was all done in VR where participants were provided an external focus cue or no cue. Results revealed that individuals jumped significantly further in RW than VR in both baseline and retention (p < .001). During training, the external group jumped significantly further than control (p < .05). These results suggest that the adoption of an external focus improves performance during training. However, we did not see a benefit of an external focus in retention. These findings should be taken into consideration when using virtual reality as a training tool when performance must be transferred to a real world environment.     

Internal reflections of an external peace process: A case study

Abstract

This case study records and analyzes how external changes, emanating from the ceasefires in Northern Ireland in 1994, resulted in significant changes within the internal world of a Northern Irish Client