This group gathers theorems of set theory, the study of sets, cardinal and ordinal numbers and the axioms that govern them. It covers comparison of the sizes of infinite sets, the axiom of choice and its equivalent forms, cardinal arithmetic, the independence of statements from the standard axioms, and descriptive set theory. A theorem belongs here when its cited article places it in set theory or states a result about sets, cardinals, ordinals or the axiom of choice.
All Set Theory
Filter Results12 entries
Sources
Jack Silver, Wikipedia
Has Member: Silver's Theorem, Section: ContributionsQuote, Has Member: Silver's Theorem, Section: Contributions
In his 1975 paper "On the Singular Cardinals Problem", Silver proved that if a cardinal κ is singular with uncountable cofinality and 2λ = λ+ for all infinite cardinals λ < κ, then 2κ = κ+.
Cantor's Theorem (Wikipedia)
Wikimedia FoundationHas Member: Cantor's Theorem, Lead sectionQuote, Has Member: Cantor's Theorem, Lead section
In mathematical set theory, Cantor's theorem is a fundamental result which
Cantor-Schroder-Bernstein theorem (Wikipedia)
Wikimedia FoundationHas Member: Cantor-Schroder-Bernstein Theorem, Lead sectionQuote, Has Member: Cantor-Schroder-Bernstein Theorem, Lead section
In set theory, the Schröder-Bernstein theorem states that
Zorn's Lemma (Wikipedia)
Wikimedia FoundationHas Member: Zorn's Lemma, Lead sectionQuote, Has Member: Zorn's Lemma, Lead section
known as the Kuratowski-Zorn lemma, is a proposition of set theory. It states that a partially ordered set containing
Kőnig's theorem (set theory) (Wikipedia)
Has Member: Konig's Theorem (Set Theory), Lead sectionQuote, Has Member: Konig's Theorem (Set Theory), Lead section
In set theory, Kőnig's theorem states that if the axiom of
Fodor's lemma, Wikipedia
Has Member: Fodor's Lemma, Lead sectionQuote, Has Member: Fodor's Lemma, Lead section
In mathematics, particularly in set theory, Fodor's lemma (or the pressing-down lemma) states:
Easton's theorem, Wikipedia
Has Member: Easton's Theorem, Lead sectionQuote, Has Member: Easton's Theorem, Lead section
In set theory, Easton's theorem is a result on the possible
Borel determinacy theorem (Wikipedia)
Has Member: Borel Determinacy Theorem, Lead sectionQuote, Has Member: Borel Determinacy Theorem, Lead section
In descriptive set theory, the Borel determinacy theorem states that any
Paul Cohen (Wikipedia)
Has Member: Cohen's Independence Theorem, Lead sectionQuote, Has Member: Cohen's Independence Theorem, Lead section
the axiom of choice are independent from Zermelo-Fraenkel set theory, for which he was awarded a Fields Medal.
Banach-Tarski Paradox (Wikipedia)
Wikimedia FoundationHas Member: Banach-Tarski Paradox, Lead sectionQuote, Has Member: Banach-Tarski Paradox, Lead section
proof of this result depends on the choice of axioms for set theory in a critical way. It can be proven using the
Transfinite Recursion Theorem (Wikipedia)
Wikimedia FoundationHas Member: Transfinite Recursion Theorem, Lead sectionQuote, Has Member: Transfinite Recursion Theorem, Lead section
sets. Since each well-ordered set is isomorphic to an ordinal, the theorem is also often stated in terms of
Absoluteness (logic) (Wikipedia)
Has Member: Shoenfield's Absoluteness Theorem, Lead sectionQuote, Has Member: Shoenfield's Absoluteness Theorem, Lead section
Issues of absoluteness are particularly important in set theory and model theory, fields where multiple structures
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.