Chain conditions, layered partial orders and weak compactness

Duration: 28 mins 19 secs

Share this media item:

Embed this media item:

<iframe width="_width_" height="_height_" src="https://sms.cam.ac.uk/media/2059787/embed" frameborder="0" scrolling="no" allowfullscreen></iframe>

Choose size:

About this item

Available Formats

About this item

Description:	Lücke, PM (Universität Bonn) Thursday 27 August 2015, 14:00-14:30


Created:	2015-09-01 16:17
Collection:	Mathematical, Foundational and Computational Aspects of the Higher Infinite
Publisher:	Isaac Newton Institute
Copyright:	Lücke, PM
Language:	eng (English)


Abstract:	Motivated by a conjecture of Todorcevic, we study strengthenings of the κ−chain conditions that are equivalent to the κ−chain condition in the case where κ is a weakly compact cardinal. We then use such properties to provide new characterizations of weakly compact cardinals. In addition, we show that the question whether weak compactness is characterized by the statement that all κ−Knaster posets satisfy these properties is independent from the axioms of ZFC. This is joint work with Sean D. Cox (VCU Richmond).

Abstract:

Motivated by a conjecture of Todorcevic, we study strengthenings of the κ−chain conditions that are equivalent to the κ−chain condition in the case where κ is a weakly compact cardinal. We then use such properties to provide new characterizations of weakly compact cardinals. In addition, we show that the question whether weak compactness is characterized by the statement that all κ−Knaster posets satisfy these properties is independent from the axioms of ZFC. This is joint work with Sean D. Cox (VCU Richmond).

Available Formats

Format	Quality	Bitrate	Size
MPEG-4 Video	640x360	1.94 Mbits/sec	412.18 MB	View	Download
WebM	640x360	590.79 kbits/sec	122.60 MB	View	Download
iPod Video	480x270	522.06 kbits/sec	108.28 MB	View	Download
MP3	44100 Hz	249.77 kbits/sec	51.86 MB	Listen	Download
Auto *	(Allows browser to choose a format it supports)