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The second continuum hypothesis, also called Luzin's hypothesis or Luzin's second continuum hypothesis, is the hypothesis that 2 ℵ 0 = 2 ℵ 1 {\displaystyle...

In mathematics, specifically set theory, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets. It states:...

2^{\aleph _{0}}<2^{\aleph _{1}}} , which is the negation of the second continuum hypothesis.: 80 : Lecture 7 : 3616  It is equivalent to a weak form of ◊...

\aleph _{0}} (aleph-null). The second smallest is ℵ 1 {\displaystyle \aleph _{1}} (aleph-one). The continuum hypothesis, which asserts that there are no...

The continuum hypothesis is independent of ZFC, a standard axiomatization of set theory; that is, it is impossible to prove the continuum hypothesis or...

The simulation hypothesis proposes that what humans experience as the world is actually a simulated reality, such as a computer simulation in which humans...

{\displaystyle (\aleph _{1},\aleph _{2},\aleph _{3},\ldots ).} His continuum hypothesis is the proposition that the cardinality c {\displaystyle {\mathfrak...

space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime...

{\displaystyle \aleph _{0},\aleph _{1},\dots } ), but unless the generalized continuum hypothesis is true, there are numbers indexed by ℵ {\displaystyle \aleph } that...

paper "The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis". In this paper, he proved that the constructible universe is an...

theory. It is implied by the continuum hypothesis, but it is consistent with ZFC and the negation of the continuum hypothesis. Informally, it says that all...

{\displaystyle {\texttt {AX}}} is equivalent to the negation of the continuum hypothesis (CH). Sierpiński's theorem answered a question of Hugo Steinhaus...

for which the continuum hypothesis fails can be solved using statistical mechanics. To determine whether or not the continuum hypothesis applies, the Knudsen...

in the aleph number hierarchy, but it follows from ZFC that the continuum hypothesis (CH) is equivalent to the identity 2ℵ0 = ℵ1. The CH states that there...

as Michael Long's interaction hypothesis, Merrill Swain's output hypothesis, and Richard Schmidt's noticing hypothesis. However, the two main areas of...

Continuum mechanics is a branch of mechanics that deals with the deformation of and transmission of forces through materials modeled as a continuous medium...

singular cardinals hypothesis (SCH) arose from the question of whether the least cardinal number for which the generalized continuum hypothesis (GCH) might fail...

the negation of the continuum hypothesis, Whitehead's problem cannot be resolved in ZFC. J. H. C. Whitehead, motivated by the second Cousin problem, first...

axiom of constructibility implies the generalized continuum hypothesis, the negation of Suslin's hypothesis, and the existence of an analytical (in fact,...

most notably, to the continuum hypothesis, which was proposed by mathematician Georg Cantor in 1873. The continuum hypothesis represents a tendency for...