Order theory is the branch of mathematics that studies sets equipped with a binary relation expressing that some elements precede others, drawing out the properties order alone allows independent of the elements' particular nature. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
Central QuestionWhich properties of a system follow from its order structure alone, so that a theorem proved in the abstract for one ordered set carries over to every other set organized the same way. 1 Key DebateHow late the abstract, general study of order came to mathematics compared with its intuitive use. Explicit study of partial orders as objects in their own right is a nineteenth-century development, arriving alongside Georg Cantor's introduction of ordinal numbers as the order types of well-ordered sets, well after mathematicians had used particular orderings, such as the ordering of the integers, for millennia. 1 Classification
Pure or Applied Connections
Associated With
Includes
Source 1/3-2/3 conjecture (Wikipedia)
Source Bourbaki-Witt theorem, Wikipedia
Source Cofinality (Wikipedia)
Source Wikipedia: Joseph Kruskal
Source Pataraia's theorem, Wikipedia
Source Wikipedia: Robert P. Dilworth
Sources
1. Wikipedia: Order Theory
Wikimedia FoundationLead section
Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations.
Partially ordered sets section
A set with a partial order on it is called a partially ordered set, poset, or just ordered set if the intended meaning is clear.
History section
The earliest explicit mentionings of partial orders are probably to be found not before the 19th century. In this context the works of George Boole are of great importance.
History
The earliest explicit mentionings of partial orders are probably to be found not before the 19th century.
View the Source Pataraia's theorem, Wikipedia
Includes: Pataraia's Theorem, LeadQuote, Includes: Pataraia's Theorem, Lead
Pataraia's theorem states each monotone map
Cofinality (Wikipedia)
Includes: Cofinality, Lead sentenceQuote, Includes: Cofinality, Lead sentence
In mathematics, especially in order theory, the cofinality cf(A) of a partially ordered set A is the least of the cardinalities of
Bourbaki-Witt theorem, Wikipedia
1/3-2/3 conjecture (Wikipedia)
Wikipedia: Joseph Kruskal
Includes: Joseph Kruskal, LeadQuote, Includes: Joseph Kruskal, Lead
Kruskal worked on well-quasi-orderings and multidimensional scaling.
Wikipedia: Robert P. Dilworth
Includes: Robert P. Dilworth, LeadQuote, Includes: Robert P. Dilworth, Lead
His primary research area was lattice theory; his biography at the MacTutor History of Mathematics archive states "it would not be an exaggeration to say that he was one of the main factors in the subject moving from being merely a tool of other disciplines to an important subject in its own right".
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