totally ordered subset

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• Ordered group — In abstract algebra, an ordered group is a group (G,+) equipped with a partial order ≤ which is translation invariant ; in other words, ≤ has the property that, for all a , b , and g in G , if a ≤ b then a+g ≤ b+g and g+a ≤ g+b . Note that… …   Wikipedia

• Ordered set — In order theory in mathematics, a set with a binary relation R on its elements that is reflexive (for all a in the set, aRa), antisymmetric (if aRb and bRa, then a = b) and transitive (if aRb and bRc, then aRc) is described as a… …   Wikipedia

• Partially ordered set — The Hasse diagram of the set of all subsets of a three element set {x, y, z}, ordered by inclusion. In mathematics, especially order theory, a partially ordered set (or poset) formalizes and generalizes the intuitive concept of an ordering,… …   Wikipedia

• well-ordered set — Math. a totally ordered set in which every nonempty subset has a smallest element with the property that there is no element in the subset less than this smallest element. Cf. partially ordered set, totally ordered set. * * * …   Universalium

• well-ordered set — Math. a totally ordered set in which every nonempty subset has a smallest element with the property that there is no element in the subset less than this smallest element. Cf. partially ordered set, totally ordered set …   Useful english dictionary

• Total order — In set theory, a total order, linear order, simple order, or (non strict) ordering is a binary relation (here denoted by infix ≤) on some set X. The relation is transitive, antisymmetric, and total. A set paired with a total order is called a… …   Wikipedia

• Axiom of choice — This article is about the mathematical concept. For the band named after it, see Axiom of Choice (band). In mathematics, the axiom of choice, or AC, is an axiom of set theory stating that for every family of nonempty sets there exists a family of …   Wikipedia

• Glossary of order theory — This is a glossary of some terms used in various branches of mathematics that are related to the fields of order, lattice, and domain theory. Note that there is a structured list of order topics available as well. Other helpful resources might be …   Wikipedia

• Hausdorff maximal principle — In mathematics, the Hausdorff maximal principle, (also called the Hausdorff maximality theorem) formulated and proved by Felix Hausdorff in 1914, is an alternate and earlier formulation of Zorn s lemma and therefore also equivalent to the axiom… …   Wikipedia

• Zorn's lemma — Zorn s lemma, also known as the Kuratowski Zorn lemma, is a proposition of set theory that states:Every partially ordered set in which every chain (i.e. totally ordered subset) has an upper bound contains at least one maximal element.It is named… …   Wikipedia

• Stable theory — For differential equations see Stability theory. In model theory, a complete theory is called stable if it does not have too many types. One goal of classification theory is to divide all complete theories into those whose models can be… …   Wikipedia