tag:www.math.bgu.ac.il,2005:/he/research/seminars/logic/meetingsלוגיקה, תורת הקבוצות וטופולוגיה, בן-גוריון נדב מאירmein@bgu.ac.ilhttps://www.math.bgu.ac.il/~mein/2016-10-30T17:20:00+02:00tag:www.math.bgu.ac.il,2005:MeetingDecorator/1852016-10-30T17:20:00+02:002016-11-03T19:51:42+02:00<span class="mathjax">Bill Chen: Tight stationarity and pcf theory - part one</span>נובמבר 8, 12:30—13:45, 2016, Math -101<div class="mathjax"><p>I will introduce the definitions of mutual and tight stationarity due to Foreman and Magidor. These notions generalize the property of stationarity from subsets of a regular cardinal to sequences of subsets of different regular cardinals (or, by some interpretations, to singular cardinals). Tight stationarity will then be related to pcf theory, and from a certain pcf-theoretic assumption we will define a ccc forcing which arranges a particularly nice structure in the tightly stationary sequences.</p></div>Bill ChenBGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/1862016-10-30T17:20:51+02:002016-11-03T19:51:31+02:00<span class="mathjax">Bill Chen: Tight stationarity and pcf theory - part two</span>נובמבר 15, 12:30—13:45, 2016, Math -101<div class="mathjax"><p>I will introduce the definitions of mutual and tight stationarity due to Foreman and Magidor. These notions generalize the property of stationarity from subsets of a regular cardinal to sequences of subsets of different regular cardinals (or, by some interpretations, to singular cardinals). Tight stationarity will then be related to pcf theory, and from a certain pcf-theoretic assumption we will define a ccc forcing which arranges a particularly nice structure in the tightly stationary sequences.</p></div>Bill ChenBGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/1942016-11-15T10:35:08+02:002016-11-15T10:41:32+02:00<span class="mathjax">Daniel Palacín: Pseudo-finite groups and centralizers</span>נובמבר 22, 12:30—13:45, 2016, Math -101<div class="mathjax"><p>In this talk I will prove that any pseudo-finite group contains an infinite abelian subgroup. Additionally, I shall also discuss some other results concerning pseudo-finite groups and centralizers.</p>
<p>This is joint work with Nadja Hempel.</p></div>Daniel Palacínhttp://math.huji.ac.il/~dpalacin/HUJItag:www.math.bgu.ac.il,2005:MeetingDecorator/2012016-11-28T09:47:54+02:002016-11-28T09:47:54+02:00<span class="mathjax">Andrés Villaveces: Around the Small Index Property on quasiminimal classes</span>נובמבר 29, 12:30—13:45, 2016, Math -101<div class="mathjax"><p>In the study of the connection between automorphism groups of models and the models themselves (or their theories, or their bi-interpretability class), the Small Index Property (SIP) has played a central role. The work of Hodges, Lascar, Shelah and Rubin among others has established in many cases when a model of a first order theory T has the Small Index Property.</p>
<p>With Ghadernezhad, we have studied this property for more general homogeneous classes. We have isolated properties of closure notions that allow to prove the SIP for some non-elementary cases, including Zilber‘s pseudo-exponentiation and other examples.</p>
<p>I will present a panorama of these results, including our more recent generalizations of the Lascar-Shelah proof of SIP for uncountable structures. This last part is joint work with Zaniar Ghadernezhad.</p></div>Andrés Villaveceshttps://avillavecesn.net/Universidad Nacional, Bogotátag:www.math.bgu.ac.il,2005:MeetingDecorator/2062016-12-04T12:17:56+02:002016-12-04T12:17:57+02:00<span class="mathjax">Misha Gavrilovich: Elementary topology via finite topological spaces</span>דצמבר 6, 12:30—13:45, 2016, Math -101<div class="mathjax"><p>We observe that several elementary definitions in point-set topology
can be reformulated in terms of finite topological spaces
and elementary category theory. This includes compactness
of Hausdorff spaces, being connected, discrete, the separation axioms.</p>
<p>Though elementary, these observations raise a few open questions.
For example, I was not able to prove that this reformulation of
compactness gives the correct answer for non-Hausdorff spaces,
or whether implications between various topological properties
can also be proved entirely in terms of finite topological spaces,
without any additional axioms.</p></div>Misha Gavrilovichhttps://www.math.bgu.ac.il/mishap.sdf.orgtag:www.math.bgu.ac.il,2005:MeetingDecorator/2092016-12-11T12:20:03+02:002016-12-13T13:39:38+02:00<span class="mathjax">Boris Zilber: Structural approximation</span>דצמבר 13, 12:15—13:30, 2016, Math -101<div class="mathjax"><p>In the framework of positive model theory I will give (recall) a definition of ``structural approximation‘‘ which is used in my paper on model-theoretic interpretation of quantum mechanics. I will then present some general theory as well as a few examples, if time permits.</p></div>Boris Zilberhttps://people.maths.ox.ac.uk/zilber/Oxfordtag:www.math.bgu.ac.il,2005:MeetingDecorator/2102016-12-14T11:50:39+02:002016-12-19T09:47:11+02:00<span class="mathjax">Menachem Kojman: Induced Ramsey Theory in inverse limits</span>דצמבר 20, 12:15—13:30, 2016, Math -101<div class="mathjax"><p>For every finite ordered graph $H$ there is a natural number $k(H)>1$ such that whenever all copies of $H$ in the ordered inverse limit of all finite ordered graphs are partitions to finitely many Borel parts, then there is a (closed) copy of the inverse limit graph in itself whose copies of $H$ meet at most $k(H)$ many parts.</p>
<p>The probability that a random ordered graph on $n$ vertices satisfies $k(H)=1$ tends to 1 as $n$ grows.</p>
<p>Joint work with S. Geschke and S. Huber.</p></div>Menachem Kojmanhttps://www.math.bgu.ac.il/~kojman/BGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/2212017-01-02T15:55:03+02:002017-01-02T15:55:03+02:00<span class="mathjax">Salma Kuhlmann: The Baer-Krull Theorem for Quasi-ordered fields</span>ינואר 3, 12:15—13:30, 2017, Math -101<div class="mathjax"><p>In my seminar talk on 29.12.2015, I introduced the notion of quasi-ordered fields, proved Fakhruddin‘s dichotomy. In this talk, I will present a version of a classical theorem in real algebra (the Baer-Krull theorem) for quasi-ordered fields.</p></div>Salma Kuhlmannhttp://www.math.uni-konstanz.de/~kuhlmann/Konstanztag:www.math.bgu.ac.il,2005:MeetingDecorator/2262017-01-09T10:37:55+02:002017-01-15T12:12:25+02:00<span class="mathjax">Assaf Hasson: A theory of pairs for weakly o-minimal non-valuational structures</span>ינואר 17, 12:15—13:30, 2017, Math -101<div class="mathjax"><p>A linearly ordered structure is weakly o-minimal if every definable set is a finite boolean combination of convex sets. A weakly o-minimal expansion of an ordered group is non-valuational if it admits no non-trivial definable convex sub-groups. By a theorem of Baizalov-Poizat if M is an o-minimal expansion of a group and N is a dense elementary substructure then the structure induced on N by all M-definable sets is weakly o-minimal non-valuational.</p>
<p>It is natural to ask whether all non-valuational structures are obtained in this way. We will give examples showing that this is not the case. We will show, however, that if M is non-valuational then there exists M^<em>, an o-minimal structure embedding M densely (as an ordered set) such that M (as a pure set) extended by all M^</em>-definable sets is precisely the structrue M. We will give a complete axiomatisation of the theory of the pair (M^<em>,M), show that it depends only on the theory of M, and that it shares many common features with the theory of dense o-minimal pairs. In particular (M^</em>,M) has dense open core (i.e., the reduct consisting only of definable open sets is o-minimal).</p>
<p>Based on joint work with E. Bar-Yehuda and Y. Peterzil.</p></div>Assaf Hassonhttps://www.math.bgu.ac.il/~hassonas/BGU