A type-free Gödel interpretation

1978 ◽  
Vol 43 (2) ◽  
pp. 213-227 ◽  
Author(s):  
Michael Beeson
Keyword(s):  
Present Author ◽  
Formal System ◽  
Constructive Mathematics ◽  
Kripke Models ◽  
Mathematical Content ◽  
Growing Body ◽  
Intended Interpretation ◽  
Close Relatives ◽  
Original Motivation ◽  
Intuitionistic Mathematics

In 1930, A. Heyting first specified a formal system for part of intuitionistic mathematics. Although his rules were presumably motivated by the “intended interpretation” or meaning of the logical symbols, over the years a number of other possible interpretations have been discovered for which the rules are also valid. In particular, one might mention the realizablity interpretation of Kleene, the (Dialectica) interpretation of Gödel, and various semantic interpretations, such as Kripke models. (Each of these has several variants or close relatives.) Each such interpretation can be regarded as defining precisely a certain “notion of constructivity”, the study of which may illuminate the still rather vague notions which underlie the intended interpretation; or, if one doubts that there is a single interpretation “intended” by all constructivist mathematicians, the study of precisely defined interpretations may help to delineate and distinguish the possibilities.In the last few years, Heyting's systems have been vastly extended, in order to encompass the large and growing body of constructive mathematics. Several kinds of new systems have been put forward and studied. The present author has extended the various realizability interpretations to several of these systems [B1], [B2] and drawn a number of interesting applications. The mathematical content of the present paper is an interpretation in the style of Godel's Dialectica interpretation, but applicable to the new systems put forward by Feferman [Fl]. The original motivation for this work was to obtain certain metamathematical applications: roughly speaking, Markov's rule and its variants.

scholarly journals SEPARATING THE FAN THEOREM AND ITS WEAKENINGS

2014 ◽  
Vol 79 (3) ◽  
pp. 792-813 ◽  
Author(s):  
ROBERT S. LUBARSKY ◽  
HANNES DIENER
Keyword(s):  
Constructive Mathematics ◽  
Kripke Models ◽  
Fan Theorem

AbstractVarieties of the Fan Theorem have recently been developed in reverse constructive mathematics, corresponding to different continuity principles. They form a natural implicational hierarchy. Some of the implications have been shown to be strict, others strict in a weak context, and yet others not at all, using disparate techniques. Here we present a family of related Kripke models which separates all of the as yet identified fan theorems.

How connected is the intuitionistic continuum?

1997 ◽  
Vol 62 (4) ◽  
pp. 1147-1150 ◽  
Author(s):  
Dirk Van Dalen
Keyword(s):  
Real Function ◽  
Peculiar Feature ◽  
Constructive Mathematics ◽  
Fan Theorem ◽  
First Time ◽  
Uniformly Continuous ◽  
Intuitionistic Mathematics ◽  
Excluded Middle ◽  
Do So ◽  
The Continuum

In the twenties Brouwer established the well-known continuity theorem “every real function is locally uniformly continuous,” [3, 2, 5]. From this theorem one immediately concludes that the continuum is indecomposable (unzerlegbar), i.e., if ℝ = A ∪ B and A ∩ B = ∅ (denoted by ℝ = A + B), then ℝ = A or ℝ = B.Brouwer deduced the indecomposability directly from the fan theorem (cf. the 1927 Berline Lectures, [7, p. 49]).The theorem was published for the first time in [6], it was used to refute the principle of the excluded middle: ¬∀x ∈ ℝ (x ∈ ℚ ∨ ¬x ∈ ℚ).The indecomposability of ℝ is a peculiar feature of constructive universa, it shows that ℝ is much more closely knit in constructive mathematics, than in classically mathematics. The classically comparable fact is the topological connectedness of ℝ. In a way this characterizes the position of ℝ: the only (classically) connected subsets of ℝ are the various kinds of segments. In intuitionistic mathematics the situation is different; the continuum has, as it were, a syrupy nature, one cannot simply take away one point. In the classical continuum one can, thanks to the principle of the excluded third, do so. To put it picturesquely, the classical continuum is the frozen intuitionistic continuum. If one removes one point from the intuitionistic continuum, there still are all those points for which it is unknown whether or not they belong to the remaining part.

‘They can’t fool me, but they can fool the others!’ Third person effect and fake news detection

2020 ◽  
Vol 35 (2) ◽  
pp. 165-180 ◽  
Author(s):  
Nicoleta Corbu ◽  
Denisa-Adriana Oprea ◽  
Elena Negrea-Busuioc ◽  
Loredana Radu
Keyword(s):  
Empirical Evidence ◽  
Presidential Elections ◽  
Fake News ◽  
Scholarly Literature ◽  
Third Person Effect ◽  
The Third ◽  
Growing Body ◽  
Third Person ◽  
Close Relatives ◽  
The Third Person

The aftermath of the 2016 US Presidential Elections and the Brexit campaign in Europe have opened the floor to heated debates about fake news and the dangers that these phenomena pose to elections and to democracy, in general. Despite a growing body of scholarly literature on fake news and its close relatives misinformation, disinformation or, more encompassing, communication and information disorders, few studies have so far attempted to empirically account for the effects that fake news might have, especially with respect to what communication scholars call the third person effect. This study aims to provide empirical evidence for the third person effect in the case of people’s self-perceived ability to detect fake news and of their perception of others’ ability to detect it. Based on a survey run in August 2018 and comprising a national, diverse sample of Romanian adults ( N = 813), this research reveals that there is a significant third person effect regarding people’s self-reported ability to spot fake news and that this effect is stronger when people compare their fake news detection literacy to that of distant others than to that close others. Furthermore, this study shows that the most important predictors of third person effect related to fake news detection are education, income, interest in politics, Facebook dependency and confirmation bias, with age being a non-significant predictor.

SEPARATING THE FAN THEOREM AND ITS WEAKENINGS II

2019 ◽  
Vol 84 (4) ◽  
pp. 1484-1509
Author(s):  
ROBERT S. LUBARSKY
Keyword(s):  
Constructive Mathematics ◽  
Kripke Models ◽  
Fan Theorem

AbstractVarieties of the Fan Theorem have recently been developed in reverse constructive mathematics, corresponding to different continuity principles. They form a natural implicational hierarchy. Earlier work showed all of these implications to be strict. Here we reprove one of the strictness results, using very different arguments. The technique used is a mixture of realizability, forcing in the guise of Heyting-valued models, and Kripke models.

Quantitative parallel EELS spectrum imaging developed as a new tool in AEM

1992 ◽  
Vol 50 (2) ◽  
pp. 1202-1203
Author(s):  
Gianluigi Botton ◽  
Gilles L'espérance
Keyword(s):  
Statistical Analysis ◽  
Spatial Resolution ◽  
Personal Computer ◽  
Systematic Study ◽  
Present Author ◽  
Chemical Elements ◽  
Detection Limits ◽  
Research Groups ◽  
Quantitative Performance ◽  
Spectrum Imaging

As interest for parallel EELS spectrum imaging grows in laboratories equipped with commercial spectrometers, different approaches were used in recent years by a few research groups in the development of the technique of spectrum imaging as reported in the literature. Either by controlling, with a personal computer both the microsope and the spectrometer or using more powerful workstations interfaced to conventional multichannel analysers with commercially available programs to control the microscope and the spectrometer, spectrum images can now be obtained. Work on the limits of the technique, in terms of the quantitative performance was reported, however, by the present author where a systematic study of artifacts detection limits, statistical errors as a function of desired spatial resolution and range of chemical elements to be studied in a map was carried out The aim of the present paper is to show an application of quantitative parallel EELS spectrum imaging where statistical analysis is performed at each pixel and interpretation is carried out using criteria established from the statistical analysis and variations in composition are analyzed with the help of information retreived from t/γ maps so that artifacts are avoided.

The observation of nano-voids in Au thin films

1987 ◽  
Vol 45 ◽  
pp. 366-367
Author(s):  
William Krakow
Keyword(s):  
Thin Films ◽  
Melting Point ◽  
Present Author ◽  
Stacking Faults ◽  
Damage Threshold ◽  
Ionic Species ◽  
Rare Gases ◽  
Chain Defects ◽  
Vacancy Chains ◽  
Au Thin Films

It has long been known that defects such as stacking faults and voids can be quenched from various alloyed metals heated to near their melting point. Today it is common practice to irradiate samples with various ionic species of rare gases which also form voids containing solidified phases of the same atomic species, e.g. ref. 3. Equivalently, electron irradiation has been used to produce damage events, e.g. ref. 4. Generally all of the above mentioned studies have relied on diffraction contrast to observe the defects produced down to a dimension of perhaps 10 to 20Å. Also all these studies have used ions or electrons which exceeded the damage threshold for knockon events. In the case of higher resolution studies the present author has identified vacancy and interstitial type chain defects in ion irradiated Si and was able to identify both di-interstitial and di-vacancy chains running through the foil.

Deficits in Selective Attention Alter Gait in Frail Older Adults

GeroPsych ◽  
2016 ◽  
Vol 29 (1) ◽  
pp. 29-36 ◽  
Author(s):  
Véronique Cornu ◽  
Jean-Paul Steinmetz ◽  
Carine Federspiel
Keyword(s):  
Older Adults ◽  
Nursing Home ◽  
Selective Attention ◽  
Dual Task ◽  
Nursing Home Residents ◽  
Gait Rehabilitation ◽  
Rehabilitation Programs ◽  
Gait Parameters ◽  
Growing Body ◽  
Task Conditions

Abstract. A growing body of research demonstrates an association between gait disorders, falls, and attentional capacities in older adults. The present work empirically analyzes differences in gait parameters in frail institutionalized older adults as a function of selective attention. Gait analysis under single- and dual-task conditions as well as selective attention measures were collected from a total of 33 nursing-home residents. We found that differences in selective attention performances were related to the investigated gait parameters. Poorer selective attention performances were associated with higher stride-to-stride variabilities and a slowing of gait speed under dual-task conditions. The present findings suggest a contribution of selective attention to a safe gait. Implications for gait rehabilitation programs are discussed.

How Do People Share Their Positive Events?

2016 ◽  
Vol 37 (4) ◽  
pp. 250-259 ◽  
Author(s):  
Cara A. Palmer ◽  
Meagan A. Ramsey ◽  
Jennifer N. Morey ◽  
Amy L. Gentzler
Keyword(s):  
Cluster Analysis ◽  
Communication Technology ◽  
Big Five ◽  
Well Being ◽  
Big Five Personality Traits ◽  
Big Five Personality ◽  
Positive Events ◽  
Growing Body ◽  
Sharing Patterns ◽  
Practical Implications

Abstract. Research suggests that sharing positive events with others is beneficial for well-being, yet little is known about how positive events are shared with others and who is most likely to share their positive events. The current study expanded on previous research by investigating how positive events are shared and individual differences in how people share these events. Participants (N = 251) reported on their likelihood to share positive events in three ways: capitalizing (sharing with close others), bragging (sharing with someone who may become jealous or upset), and mass-sharing (sharing with many people at once using communication technology) across a range of positive scenarios. Using cluster analysis, five meaningful profiles of sharing patterns emerged. These profiles were associated with gender, Big Five personality traits, narcissism, and empathy. Individuals who tended to brag when they shared their positive events were more likely to be men, reported less agreeableness, less conscientiousness, and less empathy, whereas those who tended to brag and mass-share reported the highest levels of narcissism. These results have important theoretical and practical implications for the growing body of research on sharing positive events.

Yellow Brazilian Pepper-tree Leaf Galler (suggested common name) Calophya latiforceps Burckhardt (Insecta: Hemiptera: Calophyidae: Calophyinae)

EDIS ◽  
2017 ◽  
Vol 2017 (6) ◽  
Author(s):  
James P. Cuda ◽  
Patricia Prade ◽  
Carey R. Minteer-Killian
Keyword(s):  
Biological Control ◽  
North America ◽  
Natural Enemies ◽  
Host Plants ◽  
Classical Biological Control ◽  
Biological Control Agents ◽  
Pepper Tree ◽  
Brazilian Pepper ◽  
Close Relatives ◽  
Tree Leaf

In the late 1970s, Brazilian peppertree, Schinus terebinthifolia Raddi (Sapindales: Anacardiaceae), was targeted for classical biological control in Florida because its invasive properties (see Host Plants) are consistent with escape from natural enemies (Williams 1954), and there are no native Schinus spp. in North America. The lack of native close relatives should minimize the risk of damage to non-target plants from introduced biological control agents (Pemberton 2000). [...]

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