Hilbert’s 1st problem: Is there a cardinal strictly between א0 and 2א0? Equivalently, is there A ⊆ R so that R does not inject into A, and A does not inject into N? The continuum hypothesis (CH) asserts that no such A exists. Gödel: CH is consistent with ZFC. In other words, ZFC does not prove the existence of A as above. Cohen: negation of CH also consistent with ZFC. In other words, ZFC does ...

Abstract Erdős [7] proved that the Continuum Hypothesis (CH) is equivalent to existence of an uncountable family $\mathcal {F}$ (real or complex) analytic functions, such $\big \{ f(x) \ : f \in \mathcal {F} \big \}$ countable for every x . We strengthen Erdős’ result by proving CH what we call sparse systems functions. use construct, assuming CH, equivalence relation $\sim $ on $\mathbb {R}$ a...

The position that the structure of a language has an impact on the cognition of its speakers is a venerable, if controversial, one in both linguistics and anthropology (see Gumperz and Levinson 1996 and Lucy 1992 for recent overviews). Over the last 60 years, a wide range of theories about the relationship between language and thought have been developed and disputed. The theories that posit so...

Barsalou’s (1999, 2003) perceptual symbol systems hypothesis describes how semantic knowledge is grounded in sensorimotor experience. According to the theory, knowledge is acquired through sensorimotor simulations. This challenges the classical view supported by the disembodied cognition hypothesis, which generally favours an abstract and symbolic system. We propose a unified perspective, in wh...

The ratio of CH4/CO in comets is an important indicator of the region of their formation. However, it is diicult to measure the quantity of CH4. The Giotto Ion Mass Spectrometer experiment observed a quantity of CH + which seemed inconsistent with the amount of CH4 observed. Thus, it was proposed that a source of the CH + was a distributed source in the dust. We tested this hypothesis by observ...

The hypothesis that the enlarged brain size of the primates was selected for by social, rather than purely ecological, factors has been strongly influential in studies of primate cognition and behaviour over the past two decades. However, the Machiavellian intelligence hypothesis, also known as the social brain hypothesis, tends to emphasize certain traits and behaviours, like exploitation and ...

In vivo nuclear magnetic resonance spectroscopy (NMR), a non-destructive biochemical tool used for investigating live organisms, has recently been performed in studies of the fruit fly Drosophila melanogaster, a useful model organism for investigating genetics and physiology. We used a novel high-resolution magic angle-spinning (HRMAS) NMR method to investigate live Drosophila GST2 mutants usin...

The social intelligence hypothesis suggests that living in large social networks was the primary selective pressure for the evolution of complex cognition in primates. This hypothesis is supported by comparative studies demonstrating a positive relationship between social group size and relative brain size across primates. However, the relationship between brain size and cognition remains equiv...

In the recent twenty-year retrospective issue of Animal Behavior and Cognition, Povinelli Henley (2020) argue that a host comparative studies into “complex cognition” suffer, fatally, from theoretical confusion. To rectify problem, they following challenge: alongside specifications higher-order capacity to be tested, provide hypotheses mechanism(s) necessary implement it. They spearhead this ef...

BACKGROUND Cluster headache (CH) is a neurovascular, primary headache disorder. There are, however, several case reports about patients whose CH started shortly after a structural brain disease or trauma. Motivated by a patient who developed CH 3 weeks after the removal of an eye and by similar case reports, we tested the hypothesis that the removal of an eye is a risk factor for CH. METHODS ...