ⓘ Extender (set theory)
In set theory, an extender is a system of ultrafilters which represents an elementary embedding witnessing large cardinal properties. A nonprincipal ultrafilter is the most basic case of an extender.
A κ, λextender can be defined as an elementary embedding of some model M of ZFC − ZFC minus the power set axiom having critical point κ ε M, and which maps κ to an ordinal at least equal to λ. It can also be defined as a collection of ultrafilters, one for each n tuple drawn from λ.
 printing inks KC  10 Extender an air  to  air tanker aircraft Meat extenders Media extender Seafood extender or Surimi Tele extender a secondary lens for
 Set theory is a branch of mathematical logic that studies sets which informally are collections of objects. Although any type of object can be collected
 Naïve set theory is any of several theories of sets used in the discussion of the foundations of mathematics. Unlike axiomatic set theories which are
 Musical set theory provides concepts for categorizing musical objects and describing their relationships. Howard Hanson first elaborated many of the concepts
 Neumann Bernays Godel set theory NBG is an axiomatic set theory that is a conservative extension of Zermelo Fraenkel set theory ZFC NBG introduces
 Non  well  founded set theories are variants of axiomatic set theory that allow sets to contain themselves and otherwise violate the rule of well  foundedness
 Internal set theory IST is a mathematical theory of sets developed by Edward Nelson that provides an axiomatic basis for a portion of the non  standard
 the empty set is the unique set having no elements its size or cardinality count of elements in a set is zero. Some axiomatic set theories ensure that
 In set theory a universal set is a set which contains all objects, including itself. In set theory as usually formulated, the conception of a universal

Large cardinal 
Axiom of determinacy 

Berkeley cardinal 
Core model 
Critical point (set theory) 

Extendible cardinal 
Grothendieck universe 
Huge cardinal 
Indescribable cardinal 
Ineffable cardinal 
Iterable cardinal 
Kunens inconsistency theorem 
Mahlo cardinal 
Measurable cardinal 

Rankintorank 
Reinhardt cardinal 
Remarkable cardinal 
Shelah cardinal 
Shrewd cardinal 
Strong cardinal 
Strongly compact cardinal 
Quasicompact cardinal 
Unfoldable cardinal 
Weakly compact cardinal 
Wholeness axiom 
Woodin cardinal 
Zero sharp 

Film 

Television show 

Game 

Sport 

Science 

Hobby 

Travel 

Technology 

Brand 

Outer space 

Cinematography 

Photography 

Music 

Literature 

Theatre 

History 

Transport 

Visual arts 

Recreation 

Politics 

Religion 

Nature 

Fashion 

Subculture 

Animation 

Award 

Interest 