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Set theory concept
-prewellordering. The prewellordering property is related to the stronger scale property; in practice, many pointclasses having the prewellordering property
Prewellordering
a map from A into the ordinal numbers. Each norm has an associated prewellordering, where one element of A precedes another element if the norm of the
Scale (descriptive set theory)
Scale_(descriptive_set_theory)
Topics referred to by the same term
group Norm map, a map from a pointset into the ordinals inducing a prewellordering Norm group, a group in class field theory that is the image of the
Norm
Class of mathematical orderings
generalization Ordinal number Well-founded set Well partial order Prewellordering Directed set Manolios P, Vroon D. Algorithms for Ordinal Arithmetic
Well-order
Order whose elements are all comparable
✗ ✗ Total preorder ✗ ✗ Y ✗ ✗ ✗ Y ✗ ✗ Total order ✗ Y Y ✗ ✗ ✗ Y ✗ ✗ Prewellordering ✗ ✗ Y Y ✗ ✗ Y ✗ ✗ Well-quasi-ordering ✗ ✗ ✗ Y ✗ ✗ Y ✗ ✗ Well-ordering
Total_order
determinacy, the class of inductive sets has the scale property and thus the prewellordering property. The term can have a number of different meanings: Russell's
Inductive_set
Set whose pairs have minima and maxima
✗ ✗ Total preorder ✗ ✗ Y ✗ ✗ ✗ Y ✗ ✗ Total order ✗ Y Y ✗ ✗ ✗ Y ✗ ✗ Prewellordering ✗ ✗ Y Y ✗ ✗ Y ✗ ✗ Well-quasi-ordering ✗ ✗ ✗ Y ✗ ✗ Y ✗ ✗ Well-ordering
Lattice_(order)
Reflexive and transitive binary relation
is antisymmetric and total Directed set Category of preordered sets Prewellordering Well-quasi-ordering For "proset", see e.g. Eklund, Patrik; Gähler,
Preorder
Type of binary relation
✗ ✗ Total preorder ✗ ✗ Y ✗ ✗ ✗ Y ✗ ✗ Total order ✗ Y Y ✗ ✗ ✗ Y ✗ ✗ Prewellordering ✗ ✗ Y Y ✗ ✗ Y ✗ ✗ Well-quasi-ordering ✗ ✗ ✗ Y ✗ ✗ Y ✗ ✗ Well-ordering
Transitive_relation
Binary relation that relates every element to itself
✗ ✗ Total preorder ✗ ✗ Y ✗ ✗ ✗ Y ✗ ✗ Total order ✗ Y Y ✗ ✗ ✗ Y ✗ ✗ Prewellordering ✗ ✗ Y Y ✗ ✗ Y ✗ ✗ Well-quasi-ordering ✗ ✗ ✗ Y ✗ ✗ Y ✗ ✗ Well-ordering
Reflexive_relation
Mathematical concept for comparing objects
{\displaystyle S} would constitute an infinite antichain. Better-quasi-ordering Prewellordering – Set theory concept Well-order – Class of mathematical orderings Here
Well-quasi-ordering
Mathematical ranking of a set
✗ ✗ Total preorder ✗ ✗ Y ✗ ✗ ✗ Y ✗ ✗ Total order ✗ Y Y ✗ ✗ ✗ Y ✗ ✗ Prewellordering ✗ ✗ Y Y ✗ ✗ Y ✗ ✗ Well-quasi-ordering ✗ ✗ ✗ Y ✗ ✗ Y ✗ ✗ Well-ordering
Weak_ordering
Partially ordered set equipped with a rank function
power set has the Sperner property Graded (mathematics) Prewellordering – a prewellordering with a norm is analogous to a graded poset, replacing a map
Graded_poset
Type of binary relation
✗ ✗ Total preorder ✗ ✗ Y ✗ ✗ ✗ Y ✗ ✗ Total order ✗ Y Y ✗ ✗ ✗ Y ✗ ✗ Prewellordering ✗ ✗ Y Y ✗ ✗ Y ✗ ✗ Well-quasi-ordering ✗ ✗ ✗ Y ✗ ✗ Y ✗ ✗ Well-ordering
Antisymmetric_relation
Mathematical set with an ordering
✗ ✗ Total preorder ✗ ✗ Y ✗ ✗ ✗ Y ✗ ✗ Total order ✗ Y Y ✗ ✗ ✗ Y ✗ ✗ Prewellordering ✗ ✗ Y Y ✗ ✗ Y ✗ ✗ Well-quasi-ordering ✗ ✗ ✗ Y ✗ ✗ Y ✗ ✗ Well-ordering
Partially_ordered_set
Binary relation which never occurs in both directions
✗ ✗ Total preorder ✗ ✗ Y ✗ ✗ ✗ Y ✗ ✗ Total order ✗ Y Y ✗ ✗ ✗ Y ✗ ✗ Prewellordering ✗ ✗ Y Y ✗ ✗ Y ✗ ✗ Well-quasi-ordering ✗ ✗ ✗ Y ✗ ✗ Y ✗ ✗ Well-ordering
Asymmetric_relation
Relationship between elements of two sets
✗ ✗ Total preorder ✗ ✗ Y ✗ ✗ ✗ Y ✗ ✗ Total order ✗ Y Y ✗ ✗ ✗ Y ✗ ✗ Prewellordering ✗ ✗ Y Y ✗ ✗ Y ✗ ✗ Well-quasi-ordering ✗ ✗ ✗ Y ✗ ✗ Y ✗ ✗ Well-ordering
Binary_relation
Overview of and topical guide to logic
equivalence relation Partial function Partially ordered set Preorder Prewellordering Propositional function Quasitransitive relation Reflexive relation
Outline_of_logic
Partial order with joins
✗ ✗ Total preorder ✗ ✗ Y ✗ ✗ ✗ Y ✗ ✗ Total order ✗ Y Y ✗ ✗ ✗ Y ✗ ✗ Prewellordering ✗ ✗ Y Y ✗ ✗ Y ✗ ✗ Well-quasi-ordering ✗ ✗ ✗ Y ✗ ✗ Y ✗ ✗ Well-ordering
Semilattice
Mathematical concept for comparing objects
✗ ✗ Total preorder ✗ ✗ Y ✗ ✗ ✗ Y ✗ ✗ Total order ✗ Y Y ✗ ✗ ✗ Y ✗ ✗ Prewellordering ✗ ✗ Y Y ✗ ✗ Y ✗ ✗ Well-quasi-ordering ✗ ✗ ✗ Y ✗ ✗ Y ✗ ✗ Well-ordering
Equivalence_relation
Subfield of set theory
then Π12n+1 and Σ12n+2 have the prewellordering property (and that Σ12n+1 and Π12n+2 do not have the prewellordering property, but rather have the separation
Determinacy
theory) Tree (descriptive set theory) Suslin's problem Absorption law Prewellordering Stone duality Stone's representation theorem for Boolean algebras Specialization
List_of_order_theory_topics
Smallest transitive relation containing a given binary relation
✗ ✗ Total preorder ✗ ✗ Y ✗ ✗ ✗ Y ✗ ✗ Total order ✗ Y Y ✗ ✗ ✗ Y ✗ ✗ Prewellordering ✗ ✗ Y Y ✗ ✗ Y ✗ ✗ Well-quasi-ordering ✗ ✗ ✗ Y ✗ ✗ Y ✗ ✗ Well-ordering
Transitive_closure
Property of a relation on a set
✗ ✗ Total preorder ✗ ✗ Y ✗ ✗ ✗ Y ✗ ✗ Total order ✗ Y Y ✗ ✗ ✗ Y ✗ ✗ Prewellordering ✗ ✗ Y Y ✗ ✗ Y ✗ ✗ Well-quasi-ordering ✗ ✗ ✗ Y ✗ ✗ Y ✗ ✗ Well-ordering
Connected_relation
Type of binary relation
✗ ✗ Total preorder ✗ ✗ Y ✗ ✗ ✗ Y ✗ ✗ Total order ✗ Y Y ✗ ✗ ✗ Y ✗ ✗ Prewellordering ✗ ✗ Y Y ✗ ✗ Y ✗ ✗ Well-quasi-ordering ✗ ✗ ✗ Y ✗ ✗ Y ✗ ✗ Well-ordering
Symmetric_relation
Concept in order theory
✗ ✗ Total preorder ✗ ✗ Y ✗ ✗ ✗ Y ✗ ✗ Total order ✗ Y Y ✗ ✗ ✗ Y ✗ ✗ Prewellordering ✗ ✗ Y Y ✗ ✗ Y ✗ ✗ Well-quasi-ordering ✗ ✗ ✗ Y ✗ ✗ Y ✗ ✗ Well-ordering
Join_and_meet
Type of binary relation
✗ ✗ Total preorder ✗ ✗ Y ✗ ✗ ✗ Y ✗ ✗ Total order ✗ Y Y ✗ ✗ ✗ Y ✗ ✗ Prewellordering ✗ ✗ Y Y ✗ ✗ Y ✗ ✗ Well-quasi-ordering ✗ ✗ ✗ Y ✗ ✗ Y ✗ ✗ Well-ordering
Well-founded_relation
Subfield of mathematical logic
as Kripke–Platek set theory and second-order arithmetic. Pointclass Prewellordering Scale property Kechris, Alexander S. (1994). Classical Descriptive
Descriptive_set_theory
Infinity-Borel set Lightface analytic game Perfect set property Polish space Prewellordering Projective set Property of Baire Uniformization (set theory) Universally
List_of_set_theory_topics
Topics referred to by the same term
to simplify the process of building a portfolio of financial assets Prewellordering in mathematics, a component of set theory Separation axiom in mathematics
Separation_property
Concept in mathematical logic
{\displaystyle \Theta } is also the supremum of the order types of all prewellorderings of the reals.[citation needed] It may not be obvious that it can be
Theta_(set_theory)
Infinity-Borel set Lightface analytic game Perfect set property Polish space Prewellordering Projective set Property of Baire Uniformization (set theory) Universally
List of mathematical logic topics
List_of_mathematical_logic_topics
American mathematician
of all the projective ordinals (the suprema of the lengths of all prewellorderings of the real numbers at a particular level in the projective hierarchy)
Steve_Jackson_(mathematician)
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Sapling, Newborn
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Faith; Belief; Cloud
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Jershon | ஜேரà¯à®·à¯‹à®¨
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Blacknes, Night, Destroyer, Goddess Durga in her terrifying form, A bud, Parvati
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Divine Belief
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Italian form of Hebrew Yehuwdiyth, GUIDITTA means "Jewess" or "praised."
Surname or Lastname
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English : habitational name from Fishbourne in Sussex and the Isle of Wight or Fishburn in Durham, all named from Old English fisc ‘fish’ + burna ‘stream’.In some cases, possibly a translation of Fischbach.
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Portuguese form of English Thelma, TELMA means "will."
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Defender of Mankind; Similar to Alexandra and Alexander
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A King
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