An Aronszajnline named after Nachman Aronszajn is a Total order linear ordering of cardinality math aleph 1 math which contains no subset order isomorphic to math omega 1 , math with the usual ordering the reverse of math omega 1 , math an Uncountable set uncountable subset of the Real number s with the usual ordering. Unlike Suslin s problem Suslin lines , the existence of Aronszajn lines is provable using the standard axioms of set theory. A linear ordering is an Aronszajnline if and only if it is the lexicographical ordering of some Aronszajn tree . ref cite journal title Lexicographically ordered trees last Funk first W. coauthors Lutzer, D. journal Topology and its Applications volume 152 date 2005 issue 3 pages 275 300 doi 10.1016 j.topol.2004.10.011 ref References references Category Order theory settheory stub ... more details
Infobox scientist name Nachman Aronszajn image image size caption birth date birth date 1907 07 26 df y birth place Warsaw , Congress Poland Poland death date death date and age 1980 02 05 1907 07 26 df y death place Corvallis, Oregon , United States U.S. nationality Polish American field Mathematics work institutions University of Kansas alma mater University of Warsaw br University of Paris doctoral advisor Maurice Ren Fr chet br Stefan Mazurkiewicz doctoral students W. Martin Greenlee known for Aronszajnline br Aronszajn Smith theorem br Aronszajn tree s br Reproducing kernel Hilbert space Moore Aronszajn theorem Moore Aronszajn theorem prizes religion footnotes Nachman Aronszajn 26 July ... editor last K hn ref was a Polish American mathematician of Ashkenazi Jew ish descent. Aronszajn s main ... volume 1 issue 2 year 1996 url http at.yorku.ca t o p c 06.htm . ref Aronszajn retired in 1977. He ... with Kennan T. Smith, Aronszajn offered proof of the Aronszajn Smith theorem . Also, the existence of Aronszajn trees was proven by AronszajnAronszajnline s, also named after him, are the lexicographic orderings of Aronszajn trees. He also has a fundamental contribution to the theory of reproducing kernel Hilbert space , the Reproducing kernel Hilbert space Moore Aronszajn theorem Moore Aronszajn theorem is named after him. ref Cite journal first Nachman last Aronszajn title Theory of Reproducing ... 404 year 1950 ref References Reflist External links http de.scientificcommons.org nachman aronszajn Nachman Aronszajn on Scientific Commons . http ead.diglib.ku.edu xml ksrl.ua.aronszajnnachman.html Guide to the Nachman Aronszajn Collection personal papers of Nachman Aronszajn, 1951 1977 MathGenealogy id 13097 Metadata see Wikipedia Persondata Persondata NAME Aronszajn, Nachman ALTERNATIVE NAMES ... DEFAULTSORT Aronszajn, Nachman Category 1907 births Category 1980 deaths Category American people of Polish ... stub fr Nachman Aronszajn ja pms Nachman Aronszajn pl Nachman Aronszajn ... more details
In set theory , an Aronszajn tree is an uncountable tree set theory tree with no uncountable branches and no uncountable levels. For example, every Suslin tree is an Aronszajn tree. More generally, for a cardinal , a Aronszajn tree is a tree of height such that all levels have size less than and all branches have height less than so Aronszajn trees are the same as math aleph 1 math Aronszajn trees . They are named for Nachman Aronszajn , who constructed an Aronszajn tree in 1934. A cardinal for which no Aronszajn trees exist is said to have the tree property . Sometimes the condition that is regular and uncountable is included. Existence of &kappa Aronszajn trees K nig s lemma states that math aleph 0 math Aronszajn trees do not exist. The existence of Aronszajn trees math aleph 1 math Aronszajn trees was proven by Nachman Aronszajn , and implies that the analogue of K nig s lemma does not hold for uncountable trees. The existence of math aleph 2 math Aronszajn trees is undecidable ... the existence of an math aleph 2 math Aronszajn tree, and Mitchell and Silver showed that it is consistent relative to the existence of a weakly compact cardinal that no math aleph 2 math Aronszajn trees exist. Jensen proved that V L implies that there is a Aronszajn tree in fact a Suslin tree for every ... axiom that it is consistent that no math aleph n math Aronszajn trees exist for any finite n other than 1. If is weakly compact then no Aronszajn trees exist. Conversely if is inaccessible and no Aronszajn trees exist then is weakly compact. Special Aronszajn trees An Aronszajn tree is called ... s axiom MA math aleph 1 math implies that all Aronszajn trees are special. The stronger proper forcing axiom implies the stronger statement that for any two Aronszajn trees there is a club set of levels ... sense any two Aronszajn trees are essentially isomorphic. On the other hand, it is consistent that non special Aronszajn trees exist, and this is also consistent with the generalized continuum ... more details
Wiktionary On the Line may refer to Film and television On the Line film On the Line film , a 2001 American romantic comedy On the Line 1971 film On the Line 1971 film , an American motorcycling documentary featuring Shane Stanley On the Line 1984 film On the Line 1984 film , an American Spanish Australian film featuring Stacy Sanches On the Line 1998 film On the Line 1998 film , an American TV movie starring Jeff Fahey On the Line TV series On the Line TV series , a UK sport show presented by Sally Jones Music On the Line Gary U.S. Bonds album On the Line Gary U.S. Bonds album , 1982 On the Line Michael Wycoff album On the Line Michael Wycoff album , 1983 On the Line soundtrack On the Line soundtrack , a soundtrack album from the 2001 film On the Line song On the Line song , a song by Michael Jackson On the Line , a song by Demi Lovato from Don t Forget Other uses On the Line horse , a Thoroughbred race horse, winner of the 1988 San Fernando Stakes On the Line , a novel by S. J. Rozan On the Line , a short story collection by Harvey Swados disambiguation it On the Line ... more details
Line A is name of several transport lines A New York City Subway service Line A Buenos Aires Metro Line A Prague Metro Line A Rome Metro Mexico City Metro Line A Line A EuskoTran disambig cs A linka es L nea A fr Ligne A it Linea A nl Lijn A ... more details
wiktionary Lineline lines Line or lines may refer to tocright Science and technology Line electrical engineering , a circuit or loop. A power line for electric power transmission line power or lines power, domestic mains electricity . telephone line RF transmission lineLine level , a common standard for audio signals. Line video , a measure of video display resolution or image resolution line , former name of the unit of magnetic flux, the Maxwell unit Maxwell Line unit , an obsolete unit of length equal to one twelfth or one tenth of an inch. Line geometry , an infinitely extending one dimensional figure that has no curvature. line a medical catheter , particularly one used for intravenous treatment. CVP line PICC line umbilical lineLine text file , a row of characters as a unit of organization within text files. A line of longitude or line of latitude in geography. The Line may refer ... and descent. Transport Railway line Shipping line , a company engaged in sea transport. The International Load Line or Plimsoll line Waterline , indicates the maximum safe draft for the vessel Airline A bus line, see List of bus operating companies Business Line function , a business activity. Product lining , in marketing. Military Line formation , a standard tactical formation of forces. Line infantry , a line formation of infantrymen who were part of the Line Regiments . Line of battle , in naval warfare, a line of warships, hence Ship of the line . Sports In water sports Rope Line small rope The point spread in spread betting In cricket, the direction of a delivery, see line and length . Offensive line or defensive line in American football. Racing line , in auto racing, a path taken through a corner. In kiting kite line In fishing fishing line Arts Line play Line play , a 1967 long running play written by Israel Horovitz. Line singer , a Danish singer and finalist in the Danish ... by William Wordsworth A line of text in writing or typography . Line poetry , the fundamental unit ... more details
For the San Francisco rail line also known as the T line T Third Street Context date October 2009 Unreferenced date November 2006 Image PC watercooling T Line 2009 12 03.jpg right thumb 200px Typical single waterblock DIY Watercooling setup in a PC utilizing a T Line A T line is a simple alternative to a pressure tank , air trap or any other filling, bleeding, and draining device. It is constructed by plumbing a Tee connector tri barbed, with a perpendicular secondary flow pattern, shaped like the letter T into an existing tube thus creating an alternate flow path. However, instead of routing the secondary path back into the system flow, it is simply left open or closed off using an end barb or other capping device. The tube itself thus can act as a mini reservoir and allows air bubbles to travel into it as they are caught into the Tee connector, and ultimately travel out of the system bleeding . A common use for a T Line is in a watercooling system such as those found in enthusiast PCs. The T Line is an integral part of a do it yourself watercooling system alongside the traditional choice of a reservoir. Major reasons for choosing a T Line over a standard reservoir are cost, simplicity, and space constraints. Fill Ports example The fillport by DangerDen are specifically made with T Lines in mind, and serve the purpose of capping the T line in an air tight and re openable re sealable fashion. They are available anodized in various colors and thus able to be tied in with color schemes. Category Computer hardware cooling ... more details
File A line skirt.jpg thumb right An a line skirt about the skirt dress coat style the sleeveless shirt A shirt the medical equipment Arterial catheter An A line skirt is a skirt that is fitted at the hip s and gradually widens towards the hem, giving the impression of the shape of a capital letter A. The term is also used to describe dress es and coat clothing coat s with a similar shape. ref name wwd http www.wwd.com fashion resources fashion dictionary Women s Wear Daily Glossary ref History The term was first used by the French Haute couture couture designer Christian Dior as the label for his collection of spring 1955. ref name Ward 2005 cite book last Ward first Susan title Encyclopedia of Clothing and Fashion year 2005 publisher Thomson Gale isbn 0 684 31394 4 pages 35 36 editor Steele, Valerie chapter A Line dress ref The A Line collection s feature item, then the most wanted silhouette in Paris , was a fingertip length flared jacket worn over a dress with a very full, pleated skirt . ref name Ward 2005 Although an A shape, this silhouette was not identical to what is now understood to embody the A line idea. ref name Ward 2005 That idea was given its definitive expression and popularized ... Line of spring 1958, which featured dresses flaring out dramatically from a fitted shoulder line. ref name Ward 2005 A line clothes remained popular in the 1960s and 70s, disappeared from fashion almost ... 2005 By that time, A line was used more loosely to describe any dress wider at the hips than at the bust or waist, as well as a number of flared skirt styles. ref name Ward 2005 True A line shapes ... details The A line skirt has no visible embellishments for ease, such as pleat s or slits, but is fitted to the upper hip by means of seam sewing seam s and or dart sewing dart s. However, denim A line .... The length of an A line skirt varies, between miniskirt mini and below knee length. When referring to dresses and coats, the term A line generally means fitted from the shoulder s to the hips and then widening ... more details
Infobox album See Wikipedia WikiProject Albums Name In Line Type Album Artist Bill Frisell Cover In Line.jpg Released 1983 Recorded August, 1982 Genre Post bop Length 42 22 Label ECM Producer Manfred Eicher Last album This album In Line br 1983 Next album Theoretically br 1984 Misc Extra album cover Upper caption Original LP Cover Type Album Cover In Line Original LP Cover.jpg Lower caption In Line is the debut album by Bill Frisell which was released on the ECM record label ECM label in 1983. It features four solo performances by Frisell and five duets with bassist Arild Andersen . Reception The Allmusic review awarded the album 3 stars. ref name Allmusic http www.allmusic.com album in line r138974 Allmusic Review accessed August 4, 2011. ref Album ratings rev1 Allmusic rev1Score rating 3 5 ref name Allmusic Track listing Start 5 55 Throughout 6 52 Two Arms 4 00 Shorts 3 08 Smile on You 4 07 The Beach 6 06 In Line 4 36 Three 4 17 Godson Song 3 57 All compositions by Bill Frisell Recorded August 1982 at Talent Studio, Oslo Personnel Bill Frisell guitar Arild Andersen 1, 4, 6, 8 & 9 bass References reflist Category 1983 albums Category Bill Frisell albums Category ECM Records albums Category Albums produced by Manfred Eicher pl In Line ... more details
also shown. Wikisource F hrer Directive 21 The Arkhangelsk Astrakhan line tag ref Arkhangelsk is often rendered in English language English as Archangel , its literal translation. group nb , or A A line ... line ref Boog, Horst 1996 . Germany and the Second World War The attack on the Soviet Union , http ... University Press Inc., New York. ref , as well as more rarely the Volga Arkhangelsk Astrakhan line ..., http books.google.com books?id pgVdyzKKJMC&pg PA803&dq general line volga archangel astrakhan&hl ... line Volga Archangelsk as its overall military objective. ref wikisource F hrer Directive 21 ref ... the Soviet Union up to the line Arkhangelsk Nizhny Novgorod Gorky Rostov on Don Rostov in order ... name kay The hypothetical A A line was to stretch from the port city of Arkhangelsk on the White ... military campaign before the onset of winter to the west of the line. ref name Rich Rich, Norman 1973 ... Union existed in the lands that laid to the west of the proposed A A line. ref name Rich If the line were reached, it would also be deprived of around 86 of its petroleum requirements oil territories in the Caucasus . The demarcation of the A A line as the end goal of military hostilities ... more details
Player MVP &mdash but none of the S Line s members lived to see it first awarded in 1964 65 NHL ... Trophy Hart Trophy , his wingers faltered. 1920s The Crazy Twenties were over, as was the S Line ... died first of the S Line &mdash he drowned in 1939 shortly after being hired as Habs coach at 35 ... more details
Unsourced image removed Image Patitucci Line by line.jpg Infobox Album See Wikipedia WikiProject Albums Name Line by Line Type studio Artist John Patitucci Cover John Patitucci Line by Line.jpg Released September 25, 2006 Recorded Genre Post bop Length Label JVC Victor Concord Records Concord Producer John Patitucci Last album Songs, Stories & Spirituals br 2003 This album Line by Line br 2006 Next album Remembrance br 2009 Album ratings rev1 Allmusic rev1Score rating 4 5 ref Allmusic class album id r856766 first Scott last Yanow ref rev2 All About Jazz rev2Score favorable ref cite web url http www.allaboutjazz.com php article.php?id 23912 title John Patitucci & 124 Line By Line first Martin last Gladu work allaboutjazz.com date 29 November 2006 accessdate 28 December 2011 ref Line by Line 2006 is jazz bass guitarist John Patitucci s 12th album as a sole leader, and his sixth with the Concord Records label. It features Adam Rogers , Brian Blade , Chris Potter jazz saxophonist Chris Potter , as well as a string quartet on several numbers. The record is primarily composed of Patitucci originals, except one composed by Adam Rogers, a Thelonious Monk tune, a classical piece by de Falla, and a traditional spiritual. It was recorded at Avatar Studios , New York City , and produced by John Patitucci. The album features the master bassist s best composing to date, as well as masterful work on both upright and electric bass on his part. Like several of John s revious outings, including Heart of the Bass and Communion, Line by Line is considerably versatile, spanning many time periods, styles, and emotions in music. Track listing All songs composed by John Patitucci unless otherwise noted. The Root 4 08 Agitato 4 12 Circular 6 28 Folklore 6 26 Dry September Rogers 5 54 Nana de Falla 3 27 Theme and Variations for 6 string Electric Bass and Strings 9 37 Line by Line 6 53 Evidence ... McCoy , double bass References Reflist DEFAULTSORT Line by Line Category 2006 albums Category ... more details
Infobox Film name ON LINE image ON LINE 2002 film poster.jpg caption Promotional poster for the film. writer Andrew Osborne br Jed Weintrob starring Josh Hamilton actor Josh Hamilton br Harold Perrineau br Vanessa Ferlito br Eric Millegan director Jed Weintrob distributor Indican Pictures br MGM released 2002 runtime 97 min language English On Line is a 2002 in film 2002 drama directed by Jed Weintrob and executive produced by Richard D. Titus and Tavin Marin Titus . The film was selected to world premiere at the Sundance Film Festival and was released theatrically, on DVD and television world wide. DISPLAYTITLE On Line Plot Roommates and pals John Roth Josh Hamilton actor Josh Hamilton and Moe Curley Harold Perrineau start an internet pornography adult internet site named InterconX where Jordan Nash Vanessa Ferlito is one of their stars. John has recently gone through a disastrous break up with his engagement fianc , and is now obsessed with a woman named Angel, who lives her life on 24 hour webcam . A handful of people whose lives revolve around internet relationships at an adult web site become entangled in person in this comedy drama . Cast Josh Hamilton actor Josh Hamilton as John Roth Harold Perrineau as Moe Curley Isabel Gillies as Moira Ingalls John Fleck actor John Fleck as Al Fleming Vanessa Ferlito as Jordan Nash Eric Millegan as Ed Simone Liz Owens as Angel Technology The film relies heavily on technology and in many aspects it predates or anticipates both technologies as well as cultural habits that would later become standard online practice and interaction Netiquette . The design, look and feel, animation, and programming was created by Christian D. Bruun. Programming was assisted by Steven Osit and Kate Schaffer. The technological implementations have several ... film ever to do so. External links imdb title id 0302889 title On Line http rogerebert.suntimes.com ... Official On line movie website http www.plinyminor.com Production Company website http ... more details
them in line. Bob tells Mohinder that he will be getting a partner to make sure there are no further ..., The Line earned a 4.9 11 ratings share. This episode was watched by 10.51 million viewers. fact date October 2008 References reflist Heroes Series Heroes DEFAULTSORT Line Category Heroes episodes Category 2007 television episodes es The line ... more details
A Countryman line is an Uncountable set uncountable Total order linear ordering whose square is the union of Countable set countably many Total order Chains chains . The existence of Countryman lines was first proven by Saharon Shelah Shelah . Shelah also conjectured that, assuming Proper Forcing Axiom PFA , every Aronszajnline contains a Countryman line. This conjecture, which remained open for three decades, was proven by Justin Tatch Moore Justin Moore . References cite journal last Shelah first Saharon title Decomposing uncountable squares to countably many chains journal Journal of Combinatorial Theory Series A volume 21 issue 1 year 1976 pages 110 114 authorlink Saharon Shelah doi 10.1016 0097 3165 76 90053 4 cite journal last Moore first Justin title A five element basis for the uncountable linear orders journal Annals of Mathematics 2 volume 163 issue 2 year 2006 pages 669 688 doi 10.4007 annals.2006.163.669 Category Order theory mathlogic stub ... more details
Color line may refer to Color line civil rights issue Color Line ferry operator Baseball color line disambig da Color Line de Color Line et Color Line it Color Line nl Color Line no Color Line nn Color Line fi Color Line sv Color Line ... more details
Coast Line may refer to Coast Line UP in California, United States Coast Line Denmark See also East Coast Line disambiguation West Coast Line disambiguation disambiguation ... more details
Cleveland Line may refer to the Cleveland railway line, Brisbane Cleveland railway line in Brisbane, Australia the Cleveland Line Norfolk Southern Norfolk Southern Cleveland Line in the United States disambig ... more details
Arima Line may refer to Shintetsu Arima Line , a line of Kobe Electric Railway in Japan Arima Line JGR , a line of Japanese Government Railway discontinued in 1943 disambig ... more details
General line may have the following meanings General line of the party The General Line , a 1929 Soviet film by Sergei Eisenstein General line of merchandise General line military disambig ... more details
Love on the Line may refer to Love on the Line album Love on the Line album , an album by Crazy Penis Love on the Line song Love on the Line song , a song by Blazin Squad disambig ... more details
Beaver Line may refer to Beaver Line railway , see Sharpness Branch Line Re opening proposal Beaver Line shipping , a Canadian shipping line, owner of SS Mount Temple disambig ... more details
The Pink Line is a line common to a number of rail systems. See Barcelona metro line 8 Disneyland Resort Line MTR Disneyland Resort Line , Hong Kong Pink Line Chicago Transit Authority Hammersmith & City Line , of the London Underground Line 8 Madrid Metro Sennichimae Line Osaka , Japan Viva Pink Seoul Subway Line 8 Line 13, Shanghai Metro disambig fr Ligne rose ... more details
Midland Line refers to the following rail lines Midland railway line , Perth, Australia Midland Line, New Zealand Midland Line New Haven in Massachusetts, United States disambig ... more details
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