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** Stone's representation theorem for Boolean algebras needs the Boolean prime ideal theorem.

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## Some Related Sentences

** and Stone's

__**__Ira F

**.**

__Stone's__commentary, included in

**the**new Jewish Publication Society edition of

**the**book ( ISBN 978-0-8276-0856-6 ).

** and representation

__**__In some languages,

**the**formal

__representation__of aspect is optional, and can be omitted when

**the**aspect is clear from context or does not need to be emphasized

**.**

__**__Written communication ( writing ) –

__representation__of language in a textual medium through

**the**use of a set of signs or symbols ( known as a writing system ).

__**__Lack of voting

__representation__in either House of

**the**U

**.**S

**.**Congress, as

**the**US Constitution provides these rights only to full states

**.**

__**__Parity flag in computing, indicates if

**the**number of set bits is odd or even in

**the**binary

__representation__of

**the**result of

**the**last operation

__**__Permanent Representation of Sweden to

**the**EU (, formally Sveriges ständiga

__representation__vid Europeiska unionen )

__**__occasionally with a single arrow oriented to

**the**map's

__representation__of magnetic north, or two arrows oriented to true and magnetic north respectively,

__**__

**the**Italian Senate, with a particular single-vote variant: proportional

__representation__was automatically calculated upon all losers in

**the**FPTP races, and candidates with best percentages were elected

__**__Reserved code elements under ISO 3166-1 " Codes

**for**

**the**

__representation__of names of countries and their subdivisions – Part 1: Country codes ", available on request from ISO 3166 / MA

__**__A lossless " PCM macroblock "

__representation__mode in which video data samples are represented directly, allowing perfect

__representation__of specific regions and allowing a strict limit to be placed on

**the**quantity of coded data

**for**each macroblock

**.**

__**__An enhanced lossless macroblock

__representation__mode allowing perfect

__representation__of specific regions while ordinarily using substantially fewer bits than

**the**PCM mode

**.**

__**__Flexible macroblock ordering ( FMO ), also known as slice groups, and arbitrary slice ordering ( ASO ), which are techniques

**for**restructuring

**the**ordering of

**the**

__representation__of

**the**fundamental regions ( macroblocks ) in pictures

**.**

__**__Redundant slices ( RS ), an error / loss robustness feature allowing an encoder to send an extra

__representation__of a picture region ( typically at lower fidelity ) that can be used if

**the**primary

__representation__is corrupted or lost

**.**

__**__Beginning of talks between Polish government in Warsaw with Commission of NRL about

__representation__of Greater Poland in Sejm Ustawodawczy

**.**

** and theorem

__**__Tarski's

__theorem__: For every infinite set A, there is a bijective map between

**the**sets A and A × A

**.**

__**__König's

__theorem__: Colloquially,

**the**sum of a sequence of cardinals is strictly less than

**the**product of a sequence of larger cardinals

**.**

__**__If S is a set of sentences of first-order logic and B is a consistent subset of S, then B is included in a set that is maximal among consistent subsets of S

**.**The special case where S is

**the**set of all first-order sentences in a given signature is weaker, equivalent to

**the**

**Boolean**

**prime**

**ideal**

__theorem__; see

**the**section " Weaker forms " below

**.**

__**__The Vitali

__theorem__on

**the**existence of non-measurable sets which states that there is a subset of

**the**real numbers that is not Lebesgue measurable

**.**

__**__The Baire category

__theorem__about complete metric spaces, and its consequences, such as

**the**open mapping

__theorem__and

**the**closed graph

__theorem__

**.**

__**__Gödel's completeness

__theorem__

**for**first-order logic: every consistent set of first-order sentences has a completion

**.**

__**__The numbers and are not algebraic numbers ( see

**the**Lindemann – Weierstrass

__theorem__); hence they are transcendental

**.**

__**__More generally, Rademacher's

__theorem__extends

**the**differentiability result to Lipschitz mappings between Euclidean spaces: a Lipschitz map ƒ: U → R < sup > m </ sup >, where U is an open set in R < sup > n </ sup >, is almost everywhere differentiable

**.**

__**__Artin reciprocity law, a general

__theorem__in number theory that provided a partial solution to Hilbert's ninth problem

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