[Settfa] Tuesday 04/07, <span style="font-family:sans-serif; font-size:16.6043px">Laura Wirth</span>

[kubis at math.cas.cz]

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 Tuesday 4th July, 10:00am 
 
  Place: IM in konírna 

 
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 Speaker:Laura Wirth, University of Konstanz, Germany
 Title: Archimedean Ordered Fields with(out) the Independence Property and Binary Classification

 Abstract  

 Shelah was the first to formulate a conjecture suggesting a classificationof fields without the independence property (cf. [5]). With time, this conjecture
 
has evolved, was modified, and was also specialized for the case of ordered fields(cf. [1],[2],[3],[4]). In my investigations, the focus lies on systematically examiningarchimedean ordered fields for the independence property. In this framework, Iconjecture that any archimedean ordered field without the independence propertyis real closed.
 
In my talk, I present my methods for addressing this specialized conjecture. Inparticular, I exhibit an approach for verifying the independence property and I
 
present several examples of fields that I am considering. In the end, I give a glimpseof how the independence property relates to learnability issues in the context ofbinary classification.
 
The necessary notions will be introduced.
 

 
References:
 
[1] K. Dupont, A. Hasson and S. Kuhlmann, ‘Definable valuations induced by multiplicative subgroups and NIP fields’, Arch. Math. Logic 58 (2019) 819–839.
 
[2] Y. Halevi, A. Hasson and F. Jahnke, ‘A conjectural classification of stronglydependent fields’, Bull. Symb. Log. 25 (2019) 182–195.
 
[3] Y. Halevi, A. Hasson and F. Jahnke, ‘Definable V -topologies, Henselianityand NIP’, J. Math. Log. 20 (2020).
 
[4] L. S. Krapp, S. Kuhlmann and G. Leh ?ericy, ‘Strongly NIP almost real closedfields’, MLQ Math. Log. Q. 67 (2021), 321–328.
 
[5] S. Shelah, ‘Strongly dependent theories’, Isr. J. Math. 204 (2014) 1–83.

 For more information see the seminar web page at 
 https://calendar.math.cas.cz/set-theory-and-analysis-actual .