منابع مشابه
The Continuum Hypothesis
The continuum hypotheses (CH) is one of the most central open problems in set theory, one that is important for both mathematical and philosophical reasons. The problem actually arose with the birth of set theory; indeed, in many respects it stimulated the birth of set theory. In 1874 Cantor had shown that there is a one-to-one correspondence between the natural numbers and the algebraic number...
متن کاملConsistency of the Continuum Hypothesis
One of the basic results in set theory is that the cardinality of the power set of the natural numbers is the same as the cardinality of the real numbers, which is strictly greater than the cardinality of the naturals. In fact Cantor proved a more general theorem: for any set X, the cardinality of X is strictly less than the cardinality of the power set of X. Since there is an infinite set, say...
متن کاملReconciling niche and neutrality: the continuum hypothesis.
In this study, we ask if instead of being fundamentally opposed, niche and neutral theories could simply be located at the extremes of a continuum. First, we present a model of recruitment probabilities that combines both niche and neutral processes. From this model, we predict and test whether the relative importance of niche vs. neutral processes in controlling community dynamics will vary de...
متن کاملIterated forcing and the Continuum Hypothesis
Remark. The notes which follow reflect the content of a two day tutorial which took place at the Fields Institute on 5/29 and 5/30 in 2009. Most of the content has existed in the literature for some time (primarily in the original edition of [10]) but has proved difficult to read and digest for various reasons. The only new material contained in these lectures concerns the notion of a fusion sc...
متن کاملLarge cardinals and the Continuum Hypothesis
This is a survey paper which discusses the impact of large cardinals on provability of the Continuum Hypothesis (CH). It was Gödel who first suggested that perhaps “strong axioms of infinity” (large cardinals) could decide interesting set-theoretical statements independent over ZFC, such as CH. This hope proved largely unfounded for CH – one can show that virtually all large cardinals defined s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Philosophy and Phenomenological Research
سال: 2020
ISSN: 0031-8205,1933-1592
DOI: 10.1111/phpr.12708