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Every measurable cardinal κ is a 0-huge cardinal because < sup > κ </ sup > M ⊂ M, that is, every function from κ to M is in M. Consequently, V < sub > κ + 1 </ sub >⊂ M.
Some Related Sentences
Every and measurable
Every measurable entity maps into a cardinal function but not every cardinal function is the result of the mapping of a measurable entity.
* Every set of reals in L ( R ) is Lebesgue measurable ( in fact, universally measurable ) and has the property of Baire and the perfect set property.
Every and cardinal
Every strongly inaccessible cardinal is also weakly inaccessible, as every strong limit cardinal is also a weak limit cardinal.
Every strong limit cardinal is also a weak limit cardinal, because κ < sup >+</ sup > ≤ 2 < sup > κ </ sup > for every cardinal κ, where κ < sup >+</ sup > denotes the successor cardinal of κ.
Every and is
Every legislator from Brasstown Bald to Folkston is going to have his every vote subjected to the closest scrutiny as a test of his political allegiances, not his convictions.
Every detail in his interpretation has been beautifully thought out, and of these I would especially cite the delicious laendler touch the pianist brings to the fifth variation ( an obvious indication that he is playing with Viennese musicians ), and the gossamer shading throughout.
Every taxpayer is well aware of the vast size of our annual defense budget and most of our readers also realize that a large portion of these expenditures go for military electronics.
Every few days, in the early morning, as the work progressed, twenty men would appear to push it ahead and to shift the plank foundation that distributed its weight widely on the Rotunda pavement, supported as it is by ancient brick vaulting.
Every dream, and this is true of a mental image of any type even though it may be readily interpreted into its equivalent of wakeful thought, is a psychic phenomenon for which no explanation is available.
Every library borrower, or at least those whose taste goes beyond the five-cent fiction rentals, knows what it is to hear the librarian say apologetically, `` I'm sorry, but we don't have that book.
Every community, if it is alive has a spirit, and that spirit is the center of its unity and identity.
The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.
Every natural-born citizen of a foreign state who is also an American citizen and every natural-born American citizen who is a citizen of a foreign land owes a double allegiance, one to the United States, and one to his homeland ( in the event of an immigrant becoming a citizen of the US ), or to his adopted land ( in the event of an emigrant natural born citizen of the US becoming a citizen of another nation ).
Every line of written text is a mere reflection of references from any of a multitude of traditions, or, as Barthes puts it, " the text is a tissue of quotations drawn from the innumerable centres of culture "; it is never original.
Every year, on the last Sunday in April, there is an ice fishing competition in the frozen estuarine waters of the Anadyr River's mouth.
Every lattice element of the structure is in its proper place, whether it is a single atom or a molecular grouping.
Every and because
Every pitch in the game brought forth a howl from the enraptured audience and every fly ball the visitors dropped ( and because their right fielder was still a little fuzzy from drink, they dropped many ) called forth yelps of derision.
Every Hilbert space X is a Banach space because, by definition, a Hilbert space is complete with respect to the norm associated with its inner product, where a norm and an inner product are said to be associated if for all x ∈ X.
Every week before June 19, the strip focuses on Garfield's birthday, which he dreads because of his fear of getting older.
A Girl in Every Port is considered by film scholars to be the most important film of Hawks's silent career because it is his first film to introduce many of the Hawksian themes and characters that would continue until his final films.
These languages all use special-purpose knowledge engineering because as stated by Tom Gruber, " Every ontology is a treaty-a social agreement among people with common motive in sharing.
While he admits the existence of caste-based discrimination, he writes that " Every social group cannot be regarded as a race simply because we want to protect it against prejudice and discrimination ".
The philosophe Condillac observed in 1782 that " Every science requires a special language because every science has its own ideas.
Every ball that goes into the center gate results in one spin of the slot machine, but there is a limit on the number of spins at one time because of the possibility of balls passing through the center gate while a spin is still in progress.
" In an interesting meditation on what he viewed as the harm which would result if Christian ideals were abandoned in Belgium, he said: " Every time society has distanced itself from the Gospel, which preached humility, fraternity, and peace, the people have been unhappy, because the pagan civilization of ancient Rome, which they wanted to replace it with, is based only on pride and the abuse of force " ( Commemorative speech for the war dead of the Battle of the Yser, given by Dom Marie-Albert, Abbot of Orval Abbey, Belgium, in 1936 ).
Every polynomial in can be factorized into polynomials that are irreducible over F. This factorization is unique up to permutation of the factors and the multiplication of the factors by nonzero constants from F ( because the ring of polynomials over a field is a unique factorization domain whose units are the nonzero constant polynomials ).
Every finite-dimensional normed space is reflexive, simply because in this case, the space, its dual and bidual all have the same linear dimension, hence the linear injection J from the definition is bijective, by the rank-nullity theorem.
Every finite-dimensional Hausdorff topological vector space is reflexive, because J is bijective by linear algebra, and because there is a unique Hausdorff vector space topology on a finite dimensional vector space.
# Every man shall be called fairly in turn by the list on board of prizes, because over and above their proper share, they are allowed a shift of clothes.
Every funny car has ballistic blankets covering the supercharger because this part of the engine is prone to explosion.
Harrison had a number of " trademark " phrases, such as " Morning, Mom ", " Every brand new day should be opened like a precious gift ", " Stay well, stay happy, stay right here " and " Harry Harrison wishing you the best ... because that's exactly what you deserve !” Also, on the last day of every year, Harrison would bring his four children to work with him and at the end of his shift, he would join them in giving listeners New Year's wishes.
Every weekends, lots of people are fond of going around these department stores, because their location is usually easy to visit.
Every Russian had heard of Smirnoff vodka and everyone thought it must be the best because they weren't allowed to have it.
Every morning, she visited her husband in her nightgown, which was seen as shocking, because her husband usually conferred with members of the council of state in his bed chamber at that time.
Every cognition implies necessarily a judgment, but not every judgment is necessarily cognition, because there are also judgments that are not true.
Every major political or religious event involved bloodletting because it provided a medium by which the gods could be called upon to witness and actually participate in the ceremony.
Every year, on the second Sunday of May, Tzu Chi treats this as a 3-in-1 celebration day because on this day, Buddha's Birthday, Mother's Day and Tzu Chi day is being celebrated.