\nIn this talk we’ll look at several set th eoretic issues relating to this class of models motivated by the seemingly naïve question of whether or not such models can be killed by forcing wi thout collapsing $\\omega_1$. Surprisingly the answer to this question tur ns out to be independent: under $\\mathsf{MA}_{\\aleph_1}$ no $\\omega_1$- preserving forcing can destroy Kaufmann-ness whereas under $\\diamondsuit$ there is a Kaufmann model $M$ and a Souslin tree $S$ so that forcing with $S$ adds a satisfaction class to $M$ (thus killing rather classlessness). The techniques involved in these proofs also yield another surprising sid e of Kaufmann models: it is independent of ZFC whether the class of Kaufma nn models can be axiomatized in the logic $L_{\\omega_1\, \\omega}(Q)$ whe re $Q$ is the quantifier “there exists uncountably many”. This is the logic used in Shelah’s aforementioned result\, hence the interest in thi s level of expressive power.\n LOCATION:https://researchseminars.org/talk/oxford-set-theory/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Andreas Blass (University of Michigan) DTSTART;VALUE=DATE-TIME:20201021T150000Z DTEND;VALUE=DATE-TIME:20201021T163000Z DTSTAMP;VALUE=DATE-TIME:20241112T133324Z UID:oxford-set-theory/5 DESCRIPTION:by Andreas Blass (University of Michigan) as part of Oxford Se t Theory Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/oxford-set-theory/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Mirna Džamonja (INSTITUT FOR HISTORY AND PHILOSOPHY OF SCIENCES A ND TECHNIQUES\, CNRS & UNIVERSITÉ PANTHÉON SORBONNE\, PARIS AND INSTITUT E OF MATHEMATICS\, CZECH ACADEMY OF SCIENCES\, PRAGUE) DTSTART;VALUE=DATE-TIME:20201104T160000Z DTEND;VALUE=DATE-TIME:20201104T173000Z DTSTAMP;VALUE=DATE-TIME:20241112T133324Z UID:oxford-set-theory/6 DESCRIPTION:Title: On wide Aronszajn trees\nby Mirna Džamonja (INSTITUT FOR HI STORY AND PHILOSOPHY OF SCIENCES AND TECHNIQUES\, CNRS & UNIVERSITÉ PANTH ÉON SORBONNE\, PARIS AND INSTITUTE OF MATHEMATICS\, CZECH ACADEMY OF SCIE NCES\, PRAGUE) as part of Oxford Set Theory Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/oxford-set-theory/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabriel Goldberg (Harvard University) DTSTART;VALUE=DATE-TIME:20201118T160000Z DTEND;VALUE=DATE-TIME:20201118T173000Z DTSTAMP;VALUE=DATE-TIME:20241112T133324Z UID:oxford-set-theory/7 DESCRIPTION:Title: Even ordinals and the Kunen inconsistency\nby Gabriel Goldbe rg (Harvard University) as part of Oxford Set Theory Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/oxford-set-theory/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Kameryn J Williams (UNIVERSITY OF HAWAI’I AT MĀNOA) DTSTART;VALUE=DATE-TIME:20201202T160000Z DTEND;VALUE=DATE-TIME:20201202T173000Z DTSTAMP;VALUE=DATE-TIME:20241112T133324Z UID:oxford-set-theory/8 DESCRIPTION:Title: The geology of inner mantles\nby Kameryn J Williams (UNIVERS ITY OF HAWAI’I AT MĀNOA) as part of Oxford Set Theory Seminar\n\nAbstra ct: TBA\n LOCATION:https://researchseminars.org/talk/oxford-set-theory/8/ END:VEVENT END:VCALENDAR