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- Jack_Silver abstract "Jack Howard Silver (born 23 April 1942) is a set theorist and logician at the University of California, Berkeley. He has made several deep contributions to set theory. In his 1975 paper On the Singular Cardinals Problem, Silver proved that if κ is singular with uncountable cofinality and 2λ = λ+ for all infinite cardinals λ < κ, then 2κ = κ+. Prior to Silver's proof, many mathematicians believed that a forcing argument would yield that the negation of the theorem is consistent with ZFC. He introduced the notion of master condition, which became an important tool in forcing proofs involving large cardinals. Silver proved the consistency of Chang's conjecture using the Silver collapse (which is a variation of the Levy collapse). He proved that, assuming the consistency of a supercompact cardinal, it is possible to construct a model where 2κ=κ++ holds for some measurable cardinal κ. With the introduction of the so-called Silver machines he was able to give a fine structure free proof of Jensen's covering lemma. He is also credited with discovering Silver Indiscernibles and generalizing the notion of a Kurepa tree (called Silver's Principle). He discovered 0# in his 1966 Ph.D. thesis, and the thesis is the main topic of the widely used graduate textbook Set Theory: An Introduction to Large Cardinals by Frank R. Drake. He earned his Ph.D. in Mathematics at Berkeley in 1966 under Robert Vaught. Silver's original work involving large cardinals was perhaps motivated by the goal of showing the inconsistency of an uncountable measurable cardinal; instead he was led to discover indiscernibles in L assuming a measurable cardinal exists.".
- Jack_Silver birthDate "1942-04-23".
- Jack_Silver birthPlace Missoula,_Montana.
- Jack_Silver birthYear "1942".
- Jack_Silver doctoralAdvisor Robert_Lawson_Vaught.
- Jack_Silver doctoralStudent Jeremy_Avigad.
- Jack_Silver doctoralStudent Karel_Prikry.
- Jack_Silver doctoralStudent Randall_Dougherty.
- Jack_Silver doctoralStudent William_Mitchell_(mathematician).
- Jack_Silver field Mathematics.
- Jack_Silver knownFor List_of_forcing_notions.
- Jack_Silver nationality United_States.
- Jack_Silver thumbnail Jack_Silver.jpg?width=300.
- Jack_Silver wikiPageExternalLink index.php?module=mathfacultyman&MATHFACULTY_MAN_op=sView&MATHFACULTY_id=89.
- Jack_Silver wikiPageID "21626512".
- Jack_Silver wikiPageRevisionID "596435016".
- Jack_Silver almaMater "University of California, Berkeley".
- Jack_Silver birthDate "1942-04-23".
- Jack_Silver birthPlace Missoula,_Montana.
- Jack_Silver caption "Jack Silver in 1986".
- Jack_Silver dateOfBirth "1942-04-23".
- Jack_Silver doctoralAdvisor Robert_Lawson_Vaught.
- Jack_Silver doctoralStudents Jeremy_Avigad.
- Jack_Silver doctoralStudents Karel_Prikry.
- Jack_Silver doctoralStudents Randall_Dougherty.
- Jack_Silver doctoralStudents William_Mitchell_(mathematician).
- Jack_Silver fields Mathematics.
- Jack_Silver hasPhotoCollection Jack_Silver.
- Jack_Silver knownFor List_of_forcing_notions.
- Jack_Silver name "Jack Silver".
- Jack_Silver name "Silver, Jack".
- Jack_Silver nationality United_States.
- Jack_Silver placeOfBirth Missoula,_Montana.
- Jack_Silver shortDescription "American logician".
- Jack_Silver workplaces University_of_California,_Berkeley.
- Jack_Silver description "American logician".
- Jack_Silver description "American logician".
- Jack_Silver subject Category:1942_births.
- Jack_Silver subject Category:20th-century_mathematicians.
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- Jack_Silver subject Category:American_logicians.
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- Jack_Silver subject Category:Set_theorists.
- Jack_Silver subject Category:University_of_California,_Berkeley_alumni.
- Jack_Silver subject Category:University_of_California,_Berkeley_faculty.
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- Jack_Silver comment "Jack Howard Silver (born 23 April 1942) is a set theorist and logician at the University of California, Berkeley. He has made several deep contributions to set theory. In his 1975 paper On the Singular Cardinals Problem, Silver proved that if κ is singular with uncountable cofinality and 2λ = λ+ for all infinite cardinals λ < κ, then 2κ = κ+. Prior to Silver's proof, many mathematicians believed that a forcing argument would yield that the negation of the theorem is consistent with ZFC.".
- Jack_Silver label "Jack Silver".
- Jack_Silver label "Jack Silver".
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- Jack_Silver wasDerivedFrom Jack_Silver?oldid=596435016.
- Jack_Silver depiction Jack_Silver.jpg.
- Jack_Silver givenName "Jack".
- Jack_Silver isPrimaryTopicOf Jack_Silver.
- Jack_Silver name "Jack Silver".
- Jack_Silver name "Silver, Jack".
- Jack_Silver surname "Silver".