Freely generated filters in free Boolean algebras

In this paper we will prove that ifF is a filter of a free Boolean algebra such that the minimal cardinality of the set of generators ofF is an uncountable regular cardinal or a singular cardinal with uncountable cofinality thenF is freely generated.Presented byPiotr Wojtylak     

The uniqueness of the fixed-point in every diagonalizable algebra

Summary It is well known that, in Peano arithmetic, there exists a formulaTheor (x) which numerates the set of theorems. By Gödel's and Löb's results, we have that Therefore, the considered «equations» admit, up to provable equivalence, only one solution.In this paper we prove (Corollary 1), that, in general, ifP (x) is an arbitrary formula built fromTheor (x), then the fixed-point ofP (x) (which exists by the diagonalization lemma) is unique up to provable equivalence. This result is settled referring to the concept of diagonalizable algebra (see Introduction).The algebraization of the theories which express TheorAllatum est die 3 Augustii 1975     

On the autological character of diagonalizable algebras

Summary Let be the first order theory of diagonalizable algebras. We define a bijection from the atomic formulas of (identities) to the open formulas of . is an algebraic analogous of ≒. We prove that , ^-1 preserve the validity.The algebraization of the theories which express TheorSee the precedent papers with the same subtitle.Allatum est die 21 Julii 1975     

Interpretations of the first-order theory of diagonalizable algebras in peano arithmetic

For every sequence |p _n } _n of formulas of Peano ArithmeticPA with, every formulaA of the first-order theory diagonalizable algebras, we associate a formula ⁰ A, called the value ofA inPA with respect to the interpretation. We show that, ifA is true in every diagonalizable algebra, then, for every, ⁰ A is a theorem ofPA.     

Unity in nominal equational reasoning: The algebra of equality on nominal sets

There are currently no fewer than four dedicated logics for equality reasoning over nominal sets: nominal algebra, nominal equational logic, nominal equational logic with equality only, and permissive-nominal algebra.In this survey and research paper we present these logics side-by-side in a common notation, survey their similarities and differences, discuss their proof- and model-theories, and discuss in detail what the implications of those differences are for mathematical reasoning in each of them.     

Mood-congruent free recall bias in anxious individuals is not a consequence of response bias

The status of mood-congruent free recall bias in anxious individuals was evaluated following incidental encoding of target words. Individuals with high and low levels of trait anxiety completed a modified Stroop task, which revealed an attentional bias for threat-related stimuli in anxious individuals. This group was significantly slower in naming the colour in which threat-related words were displayed compared to neutral words. In a subsequent free recall test for the words used in the modified Stroop task, anxious individuals recalled more threat-related words compared to low-anxious people. This difference was significant even when controlling for the false recall of items that had not been presented during study. These results support the view put forward by Russo, Fox, Bellinger, and Nguyen-Van-Tam (2001) that mood-congruent free recall bias in anxious individuals can be observed if the target material is encoded at a relatively shallow level. Moreover, contrary to Dowens and Calvo (2003), the current results show that the memory advantage for threat-related information in anxious individuals is not a consequence of response bias.     

Mood-congruent free recall bias in anxious individuals is not a consequence of response bias

The status of mood-congruent free recall bias in anxious individuals was evaluated following incidental encoding of target words. Individuals with high and low levels of trait anxiety completed a modified Stroop task, which revealed an attentional bias for threat-related stimuli in anxious individuals. This group was significantly slower in naming the colour in which threat-related words were displayed compared to neutral words. In a subsequent free recall test for the words used in the modified Stroop task, anxious individuals recalled more threat-related words compared to low-anxious people. This difference was significant even when controlling for the false recall of items that had not been presented during study. These results support the view put forward by Russo, Fox, Bellinger, and Nguyen-Van-Tam (2001) that mood-congruent free recall bias in anxious individuals can be observed if the target material is encoded at a relatively shallow level. Moreover, contrary to Dowens and Calvo (2003), the current results show that the memory advantage for threat-related information in anxious individuals is not a consequence of response bias.     

Prevention,not treatment,is the only hope

If our goal is the reduction or elimination of emotional disorders in our country, or in the world, a major social revolution is required. Individual psychotherapy is available to a small number only. No mass disorder has ever been eliminated by treating one person at a time. Psychotherapy is useful in teaching the possibility of unlearning damaging habits and thus it contradicts the organic-brain disease model advanced by political conservatives. Organic explanations of mental disorder find causes inside the person and ignore or deny the pathological environments of poverty, racism, sexism and exploitation. The organic model is supported by corporate power and conservative citizens' groups. It is time for radicals to come together to expose the power elite for its control of invalid ruling ideas.     

Collaborative inhibition is due to the product,not the process,of recalling in groups

Psychonomic Bulletin &; Review - When people remember together, they recall less than if they remembered separately. This is calledcollaborative inhibition. We examine whether this is due to the...     

The auditory recency advantage in longer term free recall is not enhanced by recalling prerecency items first

Gardiner and Gregg (1979) showed that in a free-recall paradigm in which each list word is embedded in a continuous stream of subject-vocalized distractor activity, recency recall was greater when the words were presented auditorily rather than visually. The experiment described here showed that this auditory advantage persisted even when list and distractor items were both spoken at a controlled pace by the experimenter, and that it was little influenced by instructions to give priority in recall either to the beginning or to the end of the list. These results strengthen the conclusion that this effect cannot be accommodated by any echoic memory theory and, because the effect was not enhanced when prerecency items were recalled first, demonstrate an additional difference between it and the somewhat similar auditory advantage found in immediate recall.     

‘You were not born here,so you are classless,you are free!’ Social class and cultural complex in analysis

The unconscious impact of differences in culture and social class is discussed from the perspective of an analyst practising in London whose ‘foreign accent’ prevents patients from placing her within the social stratifications by which they feel confined. Because she is seen by them as an analyst from both ‘inside’ and ‘outside’ the British psycho‐social fabric and cultural complex, this opens a space in the transference that enables fuller exploration of the impact of the British social class system on patients’ experience of themselves and their world. The paper considers this impact as a trans‐generational trauma of living in a society of sharp socio‐economic divisions based on material property. This is illustrated with the example of a patient who, at the point of moving towards the career to which he aspired, was unable to separate a sense of personal identity from the social class he so desperately wanted to leave behind and walk the long avenue of individuation. The dearth of literature on the subject of class is considered, and the paper concludes that not enough attention is given to class identification in training.     

Focused attention is not enough to activate discontinuities in lines, but scrutiny is

We distinguish between the roles played by spatial attention and conscious intention in terms of their impact on the processing of segmentation signals, like discontinuities in lines, associated with the act of scrutinizing. We showed previously that the processing of discontinuities in lines can be activated. This is evidenced by an impairment in the detection of a gap between parallel elements when it follows a gap between collinear elements in the same location and orientation. This effect is no longer observed if attention is divided between two gaps in the first stimulus. The results from this study show that focusing attention on a gap between collinear elements is not enough to observe a modulation, consistently with the need to integrate, rather than to separate, collinear elements in usual conditions. The modulation is sensitive to the conscious expectations of subjects, suggesting that an intention can trigger modulations that spatial attention cannot.     

The Logic of the Diamond Sutra: A is not A,therefore it is A

This paper attempts to make intelligible the logic contained in the Diamond Sutra. This 'logic' is called the 'logic of not'. It is stated in a propositional form: 'A is not A, therefore it is A'. Since this formulation is contradictory or paradoxical when it is read in light of Aristotelean logic, one might dismiss it as nonsensical. In order to show that it is neither nonsensical nor meaningless, the paper will articulate the philosophical reasons why the Sutra makes its position in this contradictory form. The thesis to be presented is that as long as one understands the 'logic of not' from a dualistic, either-or egological standpoint, it remains contradictory, but in order to properly understand it, one must effect a perspectival shift from the dualistic, egological stance to a non-dualistic, non-egological stance. This thesis is advanced with a broader concern in mind: to reexamine how the self understands itself, how it understands others, and how it understands its intra-ecological relationship with nature.     

To grit or not to grit,that is the question!

The current study tested the validity of grit as a non-cognitive construct related to, yet distinct from self-control. Data were collected from N = 1907 adults spanning the life-course (53.1% female, M age = 41.4 years). Associations between grit and present and past goals were very similar to ones observed with self-control. Extensive model tests using structural equation modeling provided evidence of substantial overlap between these two constructs, calling into question the conceptual and empirical distinctiveness of grit vis-à-vis self-control, as well as the importance of grit as a unique and independent characteristic salient for the pursuit and achievement of long-term goals. This finding was consistent and invariant across adult developmental periods. Study implications for grit-investment are discussed.