continuum hypothesis


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continuum hypothesis

n
(Mathematics) maths the assertion that there is no set whose cardinality is greater than that of the integers and smaller than that of the reals
References in periodicals archive ?
16] and it gives the optimal solution for the lineability problem for this class of surjective functions without the need of the Generalized Continuum Hypothesis.
4) For Badiou, the Continuum Hypothesis is a restrictive theorem of ontology; it confines ontology to the merely constructible and neuters the individual by reducing the power of the Axiom of Choice (BE Meditations 28 and 9).
The mathematical theory of forcing, as it is applied to the Continuum Hypothesis, provides Badiou with the paradigmatic model for the subjective response to an event.
There are questions that remain undecided by the accepted axioms of set theory (what Maddy calls the Independent Questions) that look as if they should have determinate answers; the most well-known example is Cantor's Continuum Hypothesis.
If I am right, then the 'relativity of set-theoretical notions' extends to a relativity of the truth value of 'V=L' (and, by similar arguments, of the axiom of choice and the continuum hypothesis as well) ([1983], pp.
Still, as there are (from his point of view) subuniverses in which V = L holds and subuniverses in which it does not (likewise for the continuum hypothesis and the axiom of choice), he must recognize a sense in which V = L varies in truth value.
The author has organized the main body of his text in nine chapters devoted to mathematics, analysis, commonsense sets, interpretability and logic, formalism, metamathematics, second order logic, iterative hierarchies, structuralism, sets and structures, Cantors continuum hypothesis, and a wide variety of other related subjects.
Many readers will be sympathetic to this continuum hypothesis, and recognize that it contrasts sharply with the old positivist picture of scientific reasoning, which tried unsuccessfully to find some special criteria demarcating scientific reasoning from ordinary reasoning that we apply in everyday life situations.
Still in typescript, this text contains the lecture notes for a course Cohen (1934-2007) taught at Harvard in spring 1965, shortly after his work on the continuum hypothesis.
In a famous lecture presented in 1900 at the International Congress of Mathematicians in Paris, Hilbert placed this assertion, called the continuum hypothesis, at the top of a list of the 23 most important mathematics problems of the new century.
are both interesting (especially the latter, which purports to give a principled defense of the fairly common "intuition" that formally undecidable propositions of elementary arithmetic do have determinate truth values, while the continuum hypothesis, say, does not), but hardly discussable in isolation from Field's other writings in philosophy of mathematics.
The continuum hypothesis of eating disorders seems to be a useful theory to organize thinking and research on the development of various subclinical and clinical eating disorders (Mintz et al.