# Differences

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abstracts [2013/10/20 22:42] niwinski |
abstracts [2013/11/08 10:13] (current) mostowski100 |
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** Abstract: ** The Mostowski collapse is ubiquitous in modern Set Theory. One important manifestation is in condensation principles which lie at the core of the Inner Model Program. These condensation principles are really generalizations of the Mostowski collapse and the basic open problems of the Inner Model Program can be reformulated in terms of such principles. | ** Abstract: ** The Mostowski collapse is ubiquitous in modern Set Theory. One important manifestation is in condensation principles which lie at the core of the Inner Model Program. These condensation principles are really generalizations of the Mostowski collapse and the basic open problems of the Inner Model Program can be reformulated in terms of such principles. | ||

- | [[http://www.mimuw.edu.pl/~niwinski/Haifa/Hugh.pdf|slides]] | + | {{:woodin_mostowski100.pdf|slides}} |

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stated in 1937 in the Scottish book. | stated in 1937 in the Scottish book. | ||

- | [[http://www.mimuw.edu.pl/~niwinski/Haifa/TJech.pdf|slides]] | + | {{:jech_mostowski100.pdf|slides}} |

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** Abstract: ** This talk combines two subjects which were very much in the centre of Mostowski's interests: Generalized logics and quantifiers and Set Theory. In a joint work with J.Kennedy and J. Väänänen we study the inner models of Set Theory that are obtained like the constructible universe where each stage of the construction is obtained from the previous stage by taking all definable subsets of the last stage. We get a rich collection of inner models by changing the notion of "definable" from "first order definable" to "definable by some generalized logic". The study of these inner models yields some interesting inner models and it leads to some intriguing problems. | ** Abstract: ** This talk combines two subjects which were very much in the centre of Mostowski's interests: Generalized logics and quantifiers and Set Theory. In a joint work with J.Kennedy and J. Väänänen we study the inner models of Set Theory that are obtained like the constructible universe where each stage of the construction is obtained from the previous stage by taking all definable subsets of the last stage. We get a rich collection of inner models by changing the notion of "definable" from "first order definable" to "definable by some generalized logic". The study of these inner models yields some interesting inner models and it leads to some intriguing problems. | ||

+ | {{:magidor_mostowski100.pdf|slides}} | ||

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** Abstract: ** We greatly refine work of Weisspfenning on the adeles by internalizing to ring theory the Feferman-Vaught work on restricted products( inspired in turn by Mostowski's work on products). In particular we get very precise quantifier- eliminations, using advanced work on the model theory of Henselian fields. We prove measurability of definable sets, but show that definable is not the same as locally closed. We present some extensions both of the Feferman-Vaught work,and of the Weisspfenning work, inspired by quadratic reciprocity and more general reciprocity theorems. We pay attention to uniformity over all number fields. | ** Abstract: ** We greatly refine work of Weisspfenning on the adeles by internalizing to ring theory the Feferman-Vaught work on restricted products( inspired in turn by Mostowski's work on products). In particular we get very precise quantifier- eliminations, using advanced work on the model theory of Henselian fields. We prove measurability of definable sets, but show that definable is not the same as locally closed. We present some extensions both of the Feferman-Vaught work,and of the Weisspfenning work, inspired by quadratic reciprocity and more general reciprocity theorems. We pay attention to uniformity over all number fields. | ||

+ | {{:macintyre_mostowski100.pdf|slides}} | ||

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The main focus of the talk will be on the current state of CMI. | The main focus of the talk will be on the current state of CMI. | ||

- | [[http://www.mimuw.edu.pl/~niwinski/Haifa/Harvey_last.pdf|slides]] | + | {{:friedman_mostowski100.pdf|slides}} |