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Formally, a cardinal number κ is λ-unfoldable if and only if for every transitive model M of cardinality κ of ZFC-minus-power set such that κ is in M and M contains all its sequences of length less than κ, there is a non-trivial elementary embedding j of M into a transitive model with the critical point of j being κ and j ( κ ) ≥ λ.

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## Some Related Sentences

Formally and cardinal

__Formally__

**,**

**a**measurable

__cardinal__

**is**an uncountable

__cardinal__

**number**

**κ**

**such**

**that**

**there**exists

**a**κ-additive

**,**

**non-trivial**

**,**0-1-valued measure on

**the**power

**set**

**of**

**κ**

**.**

__Formally__

**,**

**a**

__cardinal__

**κ**

**is**defined to be weakly compact

**if**it

**is**uncountable

**and**

**for**

**every**function f: < sup > 2 </ sup > →

Formally and number

__Formally__

**,**these reside

**in**

**a**complex separable Hilbert space-variously called

**the**" state space " or

**the**" associated Hilbert space "

**of**

**the**system-that

**is**well defined up to

**a**complex

__number__

**of**norm 1

**(**

**the**phase factor ).

__Formally__

**,**

**if**d

**is**

**the**dimension

**of**

**the**parameter

**,**

**and**n

**is**

**the**

__number__

**of**samples

**,**

**if**as

**and**as

**,**then

**the**

**model**

**is**semi-parametric

**.**

__Formally__

**,**

**the**word

**is**applied to persons who are publicly accepted

**in**

**a**recognised capacity

**,**

**such**as professional employment

**,**graduation from

**a**course

**of**study

**,**etc., to give

**critical**commentaries

**in**one or any

**of**

**a**

__number__

**of**specific fields

**of**public or private achievement or endeavour

**.**

__Formally__

**,**

**the**index

**of**H

**in**G

**is**defined as

**the**

__number__

**of**cosets

**of**H

**in**G

**.**

**(**The

__number__

**of**left cosets

**of**H

**in**G

**is**always equal to

**the**

__number__

**of**right cosets

**.**

__Formally__

**,**

**a**composite

__number__n = d · 2 < sup > s </ sup > + 1

**with**d

**being**odd

**is**called

**a**strong pseudoprime to

**a**relatively prime base

**a**when one

**of**

**the**following conditions hold:

__Formally__

**,**

**for**received words

**,**let denote

**the**Hamming distance between

**and**

**,**

**that**

**is**

**,**

**the**

__number__

**of**positions

**in**which

**and**differ

**.**

__Formally__

**,**

**the**use

**of**

**a**reduction

**is**

**the**function

**that**sends each natural

__number__n to

**the**largest natural

__number__m whose membership

**in**

**the**

**set**B was queried by

**the**reduction while determining

**the**membership

**of**n

**in**A

**.**

__Formally__established on October 21st

**,**1969

**,**it includes 18 departments providing 31 different undergraduate courses

**,**as well as

**a**

__number__

**of**graduate programs

**.**

__Formally__

**,**

**a**

__number__n

**is**colossally abundant

**if**

**and**

**only**

**if**

**there**

**is**an ε > 0

**such**

**that**

**for**

**all**k > 1

**,**

__Formally__

**,**

**a**natural

__number__n

**is**called highly abundant

**if**

**and**

**only**

**if**

**for**

**all**natural numbers m < n

**,**

__Formally__

**,**it refers to

**a**

**set**

**of**six verb forms inflected

**for**person

**and**

__number__forming

**a**single paradigm

**.**

__Formally__

**the**Airframe Reconditioning Squadron RNZAF

**,**

**the**unit was commercialised

**in**1998

**and**

**is**now managed by SAFE Air Ltd

**.**No

**.**1 Repair Depot was also active at

**the**base

**for**

**a**

__number__

**of**years

**,**though during

**the**war it appears to have been stationed at Hamilton

**.**

__Formally__

**,**

**the**equation above defines

**the**macroscopic neutron cross-section

**(**

**for**reaction x

**)**as

**the**proportionality constant between

**a**neutron flux incident on

**a**

**(**thin

**)**piece

**of**material

**and**

**the**

__number__

**of**reactions

**that**occur

**(**per unit volume

**)**

**in**

**that**material

**.**

__Formally__

**,**

**the**upper density

**of**

**a**graph G

**is**

**the**infimum

**of**

**the**values α

**such**

**that**

**the**finite subgraphs

**of**G

**with**density α have

**a**bounded

__number__

**of**vertices

**.**

Formally and is

__Formally__organized vocational programs supported by federal funds allow high school students to gain experience

**in**

**a**field

**of**work which

__is__likely to lead to

**a**full-time job on graduation

**.**

__Formally__

**,**

**the**

**set**

**of**

**all**context-free languages

__is__identical to

**the**

**set**

**of**languages accepted by pushdown automata

**(**PDA ).

More rigorously

**,****the**divergence**of****a**vector field F at**a****point**p__is__defined as**the**limit**of****the**net flow**of**F across**the**smooth boundary**of****a**three dimensional region V divided by**the**volume**of**V as V shrinks to p**.**__Formally__**,**__Formally__

**,**

**the**base

__is__known as Naval Support Facility Diego Garcia

**(**

**the**US activity

**)**or Permanent Joint Operating Base

**(**PJOB

**)**Diego Garcia

**(**

**the**UK's term ).

__Formally__

**,**

**there**

__is__

**a**clear distinction: " DFT " refers to

**a**mathematical transformation or function

**,**regardless

**of**how it

__is__computed

**,**whereas " FFT " refers to

**a**specific family

**of**algorithms

**for**computing DFTs

**.**

__Formally__

**,**oxidation state

__is__

**the**hypothetical charge

**that**an atom would have

**if**

**all**bonds to atoms

**of**different elements were 100 % ionic

**.**

__Formally__

**,**an inner product space

__is__

**a**vector space V over

**the**field together

**with**an inner product

**,**i

**.**e.,

**with**

**a**map

__Formally__

**,**

**if**

**M**

__is__

**a**

**set**

**,**

**the**identity function f on

**M**

__is__defined to be

**that**function

**with**domain

**and**codomain

**M**which satisfies

*

__Formally__**,**when working over**the**reals**,**as here**,**this__is__accomplished by considering**the**limit as ε → 0 ; but**the**" infinitesimal " language generalizes directly to Lie groups over general rings**.**__Formally__

**,**

**a**profinite group

__is__

**a**Hausdorff

**,**compact

**,**

**and**totally disconnected topological group:

**that**

__is__

**,**

**a**topological group

**that**

__is__also

**a**Stone space

**.**

__Formally__

**,**this sharing

**of**dynamics

__is__referred to as universality

**,**

**and**systems

**with**precisely

**the**same

**critical**exponents are said to belong to

**the**same universality class

**.**

__Formally__

**,**

**a**frame

__is__defined to be

**a**lattice L

**in**which finite meets distribute over arbitrary joins

**,**i

**.**e

**.**

**every**

**(**even infinite

**)**subset

0.158 seconds.