The mathematical subject of singular cardinals is young and many of the mathematicians who made important contributions to it are still active. This makes writing a history of singular cardinals a somewhat riskier mission than writing the history of, say, Babylonian arithmetic. Yet exactly the discussions with some of the people who created the 20th century history of singular cardinals made th...

MOND, invented by Milgrom, is a phenomenological scheme whose basic premise is that the visible matter distribution in a galaxy or cluster of galaxies alone determines its dynamics. MOND fits many observations surprisingly well. Could it be that there is no dark matter in these systems and we witness rather a violation of Newton’s universal gravity law ? If so, Einstein’s general relativity wou...

Suppose that λ = μ+ and μ is singular. We consider two aspects of the square property on subsets of λ. First, we have results which show e.g. that for א0 < κ = cf(κ) < μ, the equality cf([μ]≤κ,⊆) = μ is a sufficient condition for the set of elements of λ whose cofinality is ≤ κ to be split into the union of μ sets with squares. Secondly, we introduce a certain weak version of the square propert...

Assume GCH. Let κ = ⋃ n<ω κn, 〈κn | n < ω〉 increasing, each κn is κ n – strong witnessed by (κn, κ +n+3 n ) – extender En. We would like to force 2 = κ preserving all the cardinals and without adding new bounded subsets to κ. It was done first in [2, Sec.3]. Here we present a different method of doing this. The advantage of the present construction is that the preparation forcing is split compl...

Kapurun, a Mussulman female, aged 40 years, was admitted into hospital on the 20th October, 1889, from the Durbhunga district, having been sent by Assistant Surgeon Moti Lai Mukerji, in charge of the Laheria Serai Dispensary, Durbhunga. History.?She stated that three years ago she first noticed a swelling of the abdomen, and that it had been gradually increasing. She has had three children, all...

Moore’s law on semiconductors is coming to an end. Scaling the von Neumann architecture over the40 years of the microprocessor has led to unsustainable circuit complexity, very low compute-density,and high power consumption. On the other hand, parallel computing practices are nowhere closeto the portability, accessibility, productivity and reliability levels of single-threaded softw...