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