On critical cardinalities related to QQ-sets

In this note we collect some known information and prove new results about the small uncountable cardinal $\mathfrak q_0$. The cardinal $\mathfrak q_0$ is defined as the smallest cardinality $|A|$ of a subset $A\subset \mathbb R$ which is not a $Q$-set (a subspace $A\subset\mathbb R$ is called a $Q$-set if each subset $B\subset A$ is of type $F_\sigma$ in $A$). We present a simple proof of a folklore fact that $\mathfrak p\le\mathfrak q_0\le\min\{\mathfrak b,\mathrm{non}(\mathcal N),\log(\mathfrak c^+)\}$, and also establish the consistency of a number of strict inequalities between the cardinal $\mathfrak q_0$ and other standard small uncountable cardinals. This is done by combining some known forcing results. A new result of the paper is the consistency of $\mathfrak{p} < \mathfrak{lr} < \mathfrak{q}_0$, where $\mathfrak{lr}$ denotes the linear refinement number. Another new result is the upper bound $\mathfrak q_0\le\mathrm{non}(\mathcal I)$ holding for any $\mathfrak q_0$-flexible cccc $\sigma$-ideal $\mathcal I$ on $\mathbb R$.Comment: 8 page

PICES Press, Vol. 15, No. 2, July 2007

Contents [Individual sections are downloadable from the official URL link listed below]: PICES Science in 2007 (pdf, 0.1 Mb) 2007 Wooster Award (pdf, 0.1 Mb) FUTURE - A milestone reached but our task is not done (pdf, < 0.1 Mb) International symposium on "Reproductive and Recruitment Processes of Exploited Marine Fish Stocks" (pdf, 0.1 Mb) Recent results of the micronekton sampling inter-calibration experiment (pdf, 0.1 Mb) 2007 PICES workshop on "Measuring and monitoring primary productivity in the North Pacific" (pdf, 0.1 Mb) 2007 Harmful Algal Bloom Section annual workshop events (pdf, 0.1 Mb) A global approach for recovery and sustainability of marine resources in Large Marine Ecosystems (pdf, 0.3 Mb) Highlights of the PICES Sixteenth Annual Meeting (pdf, 0.4 Mb) Ocean acidification of the North Pacific Ocean (pdf, 0.3 Mb) Workshop on NE Pacific Coastal Ecosystems (2008 Call for Salmon Survival Forecasts) (pdf, 0.1 Mb) The state of the western North Pacific in the first half of 2007 (pdf, 0.4 Mb) PICES Calendar (pdf, 0.4 Mb) The Bering Sea: Current status and recent events (pdf, 0.3 Mb) PICES Interns (pdf, 0.3 Mb) Recent trends in waters of the subarctic NE Pacific (pdf, 0.3 Mb) Election results at PICES (pdf, 0.2 Mb) A new PICES award for monitoring and data management activities (pdf, < 0.1 Mb

PICES Press, Vol. 8, No. 1, January 2000

The state of PICES science - 1999 The status of the Bering Sea: January - July, 1999 The state of the western North Pacific in the second half of 1998 The state of the eastern North Pacific since February 1999 MEQ/WG 8 Practical Workshop Michael M. Mullin - A biography Highlights of Eighth Annual Meeting Mechanism causing the variability of the Japanese sardine population: Achievements of the Bio-Cosmos Project in Japan Climate change, global warming, and the PICES mandate – The need for improved monitoring The new age of China-GLOBEC study GLOBEC activities in Korean waters Aspects of the Global Ocean Observing System (GOOS

Expressions, Spring 2017

College of Humanities and the Arts Newsletter, Volume 1

PICES Press, Vol. 17, No. 1, January 2009

Major Outcomes from the 2008 PICES Annual Meeting: A Note from the Chairman (pdf, 0.1 Mb) PICES Science – 2008 (pdf, 0.1 Mb) 2008 PICES Awards (pdf, 0.3 Mb) Charles B. Miller – A Selective Biography (pdf, 0.4 Mb) Latest and Upcoming PICES Publications (pdf, 0.1 Mb) 2008 OECOS Workshop in Dalian (pdf, 0.2 Mb) PICES Calendar (pdf, 0.1 Mb) 2008 PICES Workshop on “Climate Scenarios for Ecosystem Modeling (II)” (pdf, 0.1 Mb) PICES/ESSAS Workshop on “Marine Ecosystem Model Inter-Comparisons” (pdf, 0.2 Mb) Highlights of the PICES Seventeenth Annual Meeting (pdf, 0.5 Mb) 2008 PICES Summer School on “Ecosystem-Based Management” (pdf, 0.3 Mb) 4th PICES Workshop on “The Okhotsk Sea and Adjacent Areas” (pdf, 0.2 Mb) PICES WG 21 Rapid Assessment Surveys (pdf, 0.4 Mb) PICES Interns (pdf, 0.3 Mb) PICES @ Oceans in a High CO2 World (pdf, 0.1 Mb) Coping with Global Change in Marine Social–Ecological Systems: An International Symposium (pdf, 0.1 Mb) The State of the Western North Pacific in the First Half of 2008 (pdf, 1.3 Mb) State of the Northeast Pacific through 2008 (pdf, 0.3 Mb) The Bering Sea: Current Status and Recent Events (pdf, 0.2 Mb) An Opinion Born of Years of Observing Timeseries Observations (pdf, 0.1 Mb) New Chairman for the PICES Fishery Science Committee (pdf, 0.1 Mb

Selective Categories and Linear Canonical Relations

A construction of Wehrheim and Woodward circumvents the problem that compositions of smooth canonical relations are not always smooth, building a category suitable for functorial quantization. To apply their construction to more examples, we introduce a notion of highly selective category, in which only certain morphisms and certain pairs of these morphisms are "good". We then apply this notion to the category $\mathbf{SLREL}$ of linear canonical relations and the result ${\rm WW}(\mathbf{SLREL})$ of our version of the WW construction, identifying the morphisms in the latter with pairs $(L,k)$ consisting of a linear canonical relation and a nonnegative integer. We put a topology on this category of indexed linear canonical relations for which composition is continuous, unlike the composition in $\mathbf{SLREL}$ itself. Subsequent papers will consider this category from the viewpoint of derived geometry and will concern quantum counterparts

Archivists with an Attitude - Rescuing the Archives from Foucault

Englis

PICES Press, Vol. 16, No. 1, January 2008

◾PICES Science in 2007 (pdf, 0.1 Mb) ◾2007 Wooster Award (pdf, 0.1 Mb) ◾FUTURE - A milestone reached but our task is not done (pdf, < 0.1 Mb) ◾International symposium on "Reproductive and Recruitment Processes of Exploited Marine Fish Stocks" (pdf, 0.1 Mb) ◾Recent results of the micronekton sampling inter-calibration experiment (pdf, 0.1 Mb) ◾2007 PICES workshop on "Measuring and monitoring primary productivity in the North Pacific" (pdf, 0.1 Mb) ◾2007 Harmful Algal Bloom Section annual workshop events (pdf, 0.1 Mb) ◾A global approach for recovery and sustainability of marine resources in Large Marine Ecosystems (pdf, 0.3 Mb) ◾Highlights of the PICES Sixteenth Annual Meeting (pdf, 0.4 Mb) ◾Ocean acidification of the North Pacific Ocean (pdf, 0.3 Mb) ◾Workshop on NE Pacific Coastal Ecosystems (2008 Call for Salmon Survival Forecasts) (pdf, 0.1 Mb) ◾The state of the western North Pacific in the first half of 2007 (pdf, 0.4 Mb) ◾PICES Calendar (pdf, 0.4 Mb) ◾The Bering Sea: Current status and recent events (pdf, 0.3 Mb) ◾PICES Interns (pdf, 0.3 Mb) ◾Recent trends in waters of the subarctic NE Pacific (pdf, 0.3 Mb) ◾Election results at PICES (pdf, 0.2 Mb) ◾A new PICES award for monitoring and data management activities (pdf, < 0.1 Mb