BOISE EXTRAVAGANZA IN SET THEORY (BEST) – Announcement 1

 The 19-th annual meeting of BEST will be hosted at Boise State University during the weekend of March 27 (Saturday) – March 29 (Monday), 2010.

It is organized by Liljana Babinkostova, Andrés E. Caicedo, Masaru Kada, and Marion Scheepers (scientific committee), and Billy Hudson (social committee).

Contributed and invited talks will be held on Saturday, Sunday and Monday at the Department of Mathematics, Boise State University. The invited speakers are:

• Justin Moore (Cornell University)
• Dilip Raghavan (University of Toronto)
• Frank Tall (University of Toronto)
• Toshimichi Usuba (University of Bonn)

The conference webpage is available here. Anyone interested in participating should contact the organizers as soon as possible by sending an email to best@math.boisestate.edu

There are three important deadlines regarding the conference:

• Lodging: The Hampton Inn & Suites is providing rooms at a reduced rate for BEST participants. To take advantage of the reduced rate, reservations must be made online by MARCH 12. After March 12 rooms will be available at prevailing rates. 
• Financial support: Limited financial support is available to partially offset lodging expenses of up to eight participants, and to partially offset lodging plus airfare expenses of up to two participants. Please see the conference website for details on applying for support. The deadline for applying for financial support is MARCH 3.
• Abstracts: Atlas Conferences, Inc. is providing abstract services for BEST 19. The deadline for submitting an abstract for invited or contributed talk is MARCH 25. Abstracts can be submitted here, and viewed here.

The conference is supported by a grant from the National Science Foundation. Abstract services are provided by Atlas Conferences, Inc. Reduced lodging

rate is provided by The Hampton Inn & Suites. Support from these entities is gratefully acknowledged.

BPFA and projective well-orderings of the reals

Sy Friedman and I recently submitted the paper and projective well-orderings of the reals to The Journal of Symbolic Logic. The preprint is available at my papers page.

In a previous paper, Boban Velickovic and I showed that if the bounded version of the proper forcing axiom, holds, then one can define a well-ordering of the reals using what is in essence a subset of as a parameter. The argument uses Justin Moore’s technique of the Mapping Reflection Principle, and provides us with a well-ordering. In this sense, the result is best possible. 

In earlier work, I had shown that is consistent with a projective well-ordering of the reals. The result with Velickovic dramatically improves this; for example, if and holds, then there is a projective well-ordering of Note that this is an implication rather than just a consistency result, and does not require that the universe is a forcing extension of The point here is that the parameter can be chosen in so that it is “projective in the codes,” and then provides us with enough coding machinery to transform the definition of the well-ordering into a projective one.

In the new paper, Friedman and I show that in fact under the projective definition is best possible, For this we need to combine the coding technique giving the well-ordering with a powerful coding device in the absence of sharps, what Friedman calls David’s trick. The point now is that the forcing required to add the witnesses that make the coding work is proper, and suffices to grant in the universe the existence of these objects.

As a technical problem, it would be interesting to see whether the appeal to the mapping reflection principle can be eliminated here. We only obtain a well-ordering in that case. Also, since turns out, perhaps unexpectedly, to provides us with definable well-orderings, it would be interesting to see that does not suffice for this.

Flashforward

Flashforward is a science-fiction novel by Canadian writer Robert Sawyer. I wanted to like the novel, I did. I first heard of it, of course, when ABC began to air commercials for their version of the story. The TV series has been kind of terrible so far. There is a lot of potential in the premise, I think, but neither the series nor the novel delivers it.

There are significant differences, too. In both cases, a global event occurs where everybody has a glimpse of their own future for a couple of minutes or so. Except for this, there is really not much in common in both cases. In the TV series, the `jump’ is six months or so. In the novel is several decades. One of the main characters finds out he is going to be killed, and when. Other than this, there is nothing much in common.

Sawyer has won several awards for his writing, but I do not understand it based on this novel. Perhaps his other works are better. In this one, what is clear is how little understanding he seems to have of the science he is using. His characters are actually well developed, and in a less plot driven story, I think his strengths would be evident. 

Here are three quotes:

Frau Drescher went as white as the snow cap on Mont Blanc. “Mein Gott,” she said. “Mein Gott.”

I mean, seriously? Ok. Perhaps that is a bit unfair; his comparisons and metaphors usually work, and his characters tend to talk like people. Let’s forget that one.

“Of course,” said Michiko. “It’s not that three minutes passed during which planes and trains and cars and assembly lines operated ithout human intervention. Rather, three minutes passed during which nothing was resolved—all the possibilities existed, stacked into shimmering whiteness. But at the end of those three minutes, consciousness returned, and the world collapsed again into a single state. And, unfortunately but inevitably, it took the single state that made the most sense, given that there had been three minutes of no consciousness: it resolved itself into the world in which planes and cars had crashed. But the crashes didn’t occur during those three minutes; they never occurred at all. We simply went in one jump from the way things were before to the way they were after.”

“That’s… that’s crazy,” said Lloyd.

[...]

“No, it’s not. It’s quantum physics.”

No, it’s not. It’s crazy. It’s just absurd. It is what happens when rather than understanding the science, one takes the metaphors scientists use and erroneously assumes they are literal truths. The TV series quickly distanced itself from this nonsense. In the book, only humans see the future, since they are the only ones with “consciousness.” And no recording devices work during the `jump’, because nobody is observing them. Seriously. Sawyer seems to think that the tree actually makes no sound. Or, perhaps, there isn’t even a forest, if nobody is watching it. It gets worse, because of course it is not only quantum mechanics that is thoroughly misunderstood. 

Surely all consciousness everywhere had to agree on what constituted “now.”

This being what the main physicist of the story thinks. Everywhere being, of course, the entire universe. This in the same paragraph where the physicist explains some relativity theory to himself. 

Sigh.

Why dose nobody ask the students

From Tampa Bay Times, October 1, 2009, page T10.

A student’s letter to tbt*

Editor’s note: On Monday, tbt* published a story describing President Obama’s desire to increase the number of days U.S. children go to school each year. A junior at a Pasco high school e-mailed the following response — with the subject line “why dose nobody ask the students’’ — to tbt*. It is printed here, unedited:

Dear “tbt” editor of which it may concern I’m a student of pasco coun ty a junior to be precise and pleas do not mistake this for a Dear Abby seg ment I am not a 40 year old women concerned about her felines. I am just appalled as a member of the student body that in ever y in other words the only article I could find of president Obahmas plan to extend the school year, school days, and e ven rumored around school of mak ing us work weekends that they have not a single students opinion on the subject.

more so that they believe that the school boards “research” should stand as good evidence of the im provement in our “higher achieve ment”. a very intelligent man once said if you obser ve you have therefor changed the out come (now notice I didn’t abbreviate that phrase as I did the other stated phrases that’s because it’s not exact not as an in sult to any of the readers but some would use this against the students to further there pointless war against other country’s grade average).

at any rate not only do I belie ve it to be unreliable research but I also believe it dose not properly address to how our mind will adjust to the added stress. now personally I don’t ge t what in heavens name these peo ple they put in these articles have to do with the students spending more time in school it’s not like there stuck in the classroom ding the e xtra work the teachers prepare to compensate for the e xtra time. are they siting first row in this teenage bomb they’re building.

the plan reducing summer well first why don’t they come clean that they all ready reduced it we’re only on vacation for two months give or take a few days and for years they lied to our faces saying we have three months vaca.

to sum it all up I just wish he pub lic the pollutions the school board the reporters would address us on things that affect US not them now granted there may have been a seg ment on the news some were that addressed students about it but if there was did you even pay attention. and let me end this by saying the subduction of certain rights in order to maintain the learning enviorment making your usage of the 1 st amend ment right lesser then you would have in normal society is the same as removing them at the front step!

(I would like to stay anonymous)

Three-player perfect information games are usually undetermined

Recently, I gave the talk Undeterminacy and choice (Indeterminación y elección), at the XVII Colombian Mathematical Congress, in Cali. Slides can be found at my talks page.

The talk addressed the results of my recent paper on with Richard Ketchersid, mentioned in my previous entry, and some extensions, about which I expect to be posting soon. Afterwards, somebody asked me how much of the theory of determinacy can be extended to three-player (or more) perfect information games. Not much.

The following easy example was suggested by Richard Ketchersid: There is an undetermined one-move game where players I, II, III play 0 or 1, with I playing first, then II, and finally III. To see this, say that and are the numbers played, and that:

• Player I wins iff
• Player II wins iff and
• Player III wins if

(One may think of this game as a perfect information version of paper-rock-scissors.) I imagine this observation is ancient, and would be grateful for a reference.

A trichotomy theorem in natural models of AD+

[Updated: July 24, 2009]

Richard Ketchersid and I have submitted the paper A trichotomy theorem in natural models of  to the Proceedings of BEST. The preprint is available at my papers page. In the paper we provide references and background for the results we discuss, so here I will only mention briefly what the paper is about.

is a strengthening, due to Woodin, of the more familiar axiom of determinacy. In all known models of determinacy, it is the case that in fact holds. Since is an axiom about sets of reals, its natural models are those of the form although there are models of not of this form. 

In this paper, we prove the following result:

Theorem. Assume that and that holds. Let be any partially ordered set. Then either there is an injection of the full binary tree into such that no two points in its image are -comparable, or else can be written as a well-ordered union of -chains.

This statement should be reminiscent of the Harrington-Marker-Shelah theorem on Borel orderings, and in a sense our argument is a generalization of this result. 

Two corollaries are worth pointing out: Suppose first that is simply the diagonal on Then the theorem gives us:

Corollary. Assume that and that holds. Let be a set. Then either injects into or else is well-orderable.

This can be seen as a generalization of Silver’s theorem on co-analytic equivalence relation. In particular, we have the following basis result:

Corollary. Assume that and that holds. Then injects into every infinite set, and if is uncountable, then either or injects into

Our arguments make use of technology developed by Woodin. First, any model of of the form either satisfies or else it has the form for some set of ordinals.

In the second case, one argues via an analysis of the -Borel sets. Essentially, one uses what is sometimes called code compression to obtain, given an -Borel code for a set local versions of this code, that are sufficiently absolute in that they compute traces of correctly both in small inner models of choice, and their forcing extensions. Once this is obtained, the result essentially follows from soft forcing arguments as if the original sets under consideration were Borel. 

In the first case, one uses the argument above to see that a set is expressible as a well-ordered union of smaller sets, for which the result applies. This uses that, under models of the form are of the form where denotes the family of countable bounded subsets of One then uses the uniqueness of the supercompactness measures on for to “paste together” the smaller pieces that make up in a coherent way. The idea in this case was suggested by Woodin, and it is surprisingly flexible. 

As an application, we consider the countable-finite game due to Scheepers. In this game, one fixes a set and two players, I and II, alternate for -many moves, with I moving first, so that each move of I is a countable subset of and each move of II is a finite subset of Player II wins if and only if the union of the finite sets covers the union of the countable sets. If choice holds, it is obvious that player II has a winning strategy. The same argument shows that, without choice, player II has a winning strategy when is countable. In contrast, we prove:

Corollary. Assume that and that holds. Then the countable-finite game on is undetermined for all uncountable sets

For a brief presentation of these results, see the talks that Richard and I gave at BEST 18, available here or at my talks page.

(The “trichotomy” in the title refers to an additional clause in the main theorem, related to the Glimm-Effros dichotomy. I expect to post about an extension of this part of the result soon.)

BOISE EXTRAVAGANZA IN SET THEORY (BEST) -Announcement 3 and Call for papers

Announcement 3: Call for papers, Lodging Deadlines.

The 18-th annual meeting of BEST will be hosted at Boise State University during the weekend of March 27 (Friday) – March 29 (Sunday), 2009. It is organized by Liljana Babinkostova, Andres Caicedo, Stefan Geschke, Richard Ketchersid, and Marion Scheepers. Contributed and invited talks will be held on Friday, Saturday and Sunday at the Department of Mathematics, Boise State University. The four invited speakers are:

Steve Jackson (University of North Texas)

Ljubisa Kocinac (University of Nis, Republic of Serbia)

Assaf Rinot (Tel Aviv University, Israel)

Grigor Sargsyan (University of California, Berkeley)

Please consult the conference webpage at URL

http://math.boisestate.edu/~best/best18

There are three remaining important deadlines regarding the conference. CRITICAL DEADLINE: LODGING: The Hampton Inn & Suites is providing rooms at a reduced rate for BEST participants. To take advantage of the reduced rate, reservations must be made online by MARCH 12. Please follow this link to the Hampton Inn’s online reservation site for BEST. Anyone interested in participating should contact the organizers as soon as possible by sending an email to

best@math.boisestate.edu

DEADLINE 2: Abstracts: Atlas Conferences, Inc. is providing abstract services for BEST 18. The deadline for submitting an abstract for invited or contributed talk is MARCH 25. Links are available at the BEST 18 web site. DEADLINE 3: Call for papers: The organizers will be editors for a volume in the Contemporary Mathematics series. Research papers on topics related to Set Theory and its Applications will be considered for publication in this volume. All papers will go through a thorough referee process. Former and current participants of the BEST conferences or their collaborators are especially encouraged to consider submitting a research paper. Anyone interested in submitting a paper should contact Marion Scheepers as soon as possible at

marion@math.boisestate.edu

with this information. Subsequently information regarding preparation of papers will be sent to contributing authors by Contemporary Mathematics. The deadline for submitting a paper is JULY 21. On Saturday, March 28, Billy and Kris Hudson will host a social gathering at their home. All participants are cordially invited to ths social event. Kindly inform Billy at e-mail address

billyhudson@boisestate.edu

of plans to attend. More information is available at the conference web site. The conference is supported by a grant from the National Science Foundation. Abstract services are provided by Atlas Conferences, Inc. Contemporary Mathematics is published by the American Mathematical Society. Reduced lodging rate is provided by The Hampton Inn & Suites. Support from these entities is gratefully acknowledged.

Steel VIG (January 30-February 1, 2009)

 

John Steel was one of my advisors at UC Berkeley. The fifteenth Very Informal Gathering of Logicians at UCLA (VIG) was in honor of John Steel on his 60th birthday. 

The meeting was excellent, with some very interesting talks and nice shared memories. Plus, Benjamin Miller worked miracles and secured the photo above without John finding out.

BOISE EXTRAVAGANZA IN SET THEORY – Announcement 2, Call for papers

The 18-th annual meeting of BEST will be hosted at Boise State University during the weekend of March 27 (Friday) – March 29 (Sunday), 2009.

It is organized by Liljana Babinkostova, Andres Caicedo, Stefan Geschke, Richard Ketchersid and Marion Scheepers.

Contributed and invited talks will be held on Friday, Saturday and Sunday at the Department of Mathematics, Boise State University. The four invited speakers are:

Steve Jackson (University of North Texas)

Ljubisa Kocinac (University of Nis, Republic of Serbia)

Assaf Rinot (Tel Aviv University, Israel)

Grigor Sargsyan (University of California, Berkeley)

The conference webpage is available at URL

http://math.boisestate.edu/~best/best18

There are four important deadlines regarding the conference:

Lodging: The Hampton Inn & Suites is providing rooms at a reduced rate for BEST participants. To take advantage of the reduced rate, reservations must be made online by MARCH 12. Follow this link for the Hampton Inn’s online reservation site for BEST.

Financial support: Limited financial support is available to partially offset travel expenses of some participants. The criteria for granting support include whether the participant has alternative financial support for the conference, and whether the participant is presenting a talk at the conference. Preference is given to graduate students and early career researchers. The amount of support is contingent on the budget constraints. University accounting regulations require completing certain forms online BEFORE the conference, and submitting original receipts of expenses. Reimbursements will be sent after the conference. The deadline for applying for financial support is MARCH 3.

To apply for support, email the organizers at

best@diamond.boisestate.edu

Applications from graduate students must be supported by a separate email from their thesis advisor. Anyone interested in participating should contact the organizers as soon as possible by sending an email to

best@math.boisestate.edu

Abstracts: Atlas Conferences, Inc. is providing abstract services for BEST 18. The deadline for submitting an abstract for invited or contributed talk is MARCH 25. Links are available at the BEST 18 web site.

Call for papers: The organizers will be editors for a volume in the Contemporary Mathematics series. Research papers on topics related to Set Theory and its Applications will be considered for publication in this volume.

All papers will go through a thorough referee process. Former and current participants of the BEST conferences or their collaborators are especially encouraged to consider submitting a research paper. Anyone interested in submitting a paper should contact Marion Scheepers as soon as possible at 

marion@math.boisestate.edu 

with this information. Subsequently information regarding preparation of papers will be sent to contributing authors by Contemporary Mathematics. The deadline for submitting a paper is JULY 21.

The conference is supported by a grant from the National Science Foundation. Abstract services are provided by Atlas Conferences, Inc. Contemporary Mathematics is published by the American Mathematical Society. Reduced lodging rate is provided by The Hampton Inn & Suites. Support from these entities is gratefully acknowledged.

BOISE EXTRAVAGANZA IN SET THEORY – Announcement 1

 Friday, March 27 – Sunday, March 29, 2009

Organized by Liljana Babinkostova, Andres Caicedo, Stefan Geschke, Richard Ketchersid, and Marion Scheepers.

We are pleased to announce our eighteenth annual BEST conference.

There will be four talks by invited speakers:

Steve Jackson (University of North Texas)

Ljubisa Kocinac (University of Nis, Republic of Serbia)

Assaf Rinot (Tel Aviv University, Israel)

Grigor Sargsyan (University of California, Berkeley)

The talks will be held on Friday, Saturday and Sunday at the Department of Mathematics, Boise State University.

The conference webpage is available at URL

http://math.boisestate.edu/~best/best18

This page will be updated with information regarding lodging, abstract submission, weather, maps, schedule, etc. 

Limited financial support is available to partially offset travel expenses of some participants. The criteria for granting support include whether the participant has alternative financial support for the conference, and whether the participant is presenting a talk at the conference. Preference is given to graduate students and early career researchers. The amount of support is contingent on the budget constraints. University accounting regulations require completing certain forms appropriately and submitting original receipts of expenses before issuing checks.  

To apply for support, email the organizers at

best@math.boisestate.edu 

Applications from graduate students must be supported by a separate email from their thesis advisor. 

Anyone interested in participating should contact the organizers as soon as possible by sending an email to

best@math.boisestate.edu

The organizers will be editors for a volume in the Contemporary Mathematics series. Research papers on topics related to Set Theory and its Applications will be considered for publication in this volume. All papers will go through a thorough referee process. Former and current participants of the BEST conferences or their collaborators are especially encouraged to consider submitting a research paper. Anyone interested in submitting a paper should contact Marion Scheepers as soon as possible at marion@math.boisestate.edu with this information. More information will be posted at the conference web site.

The conference is supported by a grant from the National Science Foundation. Abstract services are provided by Atlas Conferences, Inc. Contemporary Mathematics is published by the American Mathematical Society. Support from these three organizations is gratefully acknowledged.