University Seminar: Logic Across Disciplines

Spring 2020

Title: What is the difference between the sets of primes?
Speaker: Alexandra Shlapentokh, East Carolina University
http://myweb.ecu.edu/shlapentokha/
Date and Time: Monday, March 9, 3:45PM-5:00PM
Place: Phillips Hall (801 22nd Street), Room 736
 

Abstract:  We will discuss the history and recent developments concerning definability and decidability problems over subrings of the field of rational numbers.


Title: The tree method for priority arguments
Speaker: Valentina Harizanov, GWU
Date and Time:  Friday, March 27, 12:30PM-1:30PM
Place: Phillips Hall (801 22nd Street), Room 736
 

Abstract:  We will introduce a tree construction for a priority argument by introducing a priority tree in which every node has a strategy for satisfying a corresponding requirement. At the end, we define a true path, which in the case of the finite injury argument can be computed using the halting set. The nodes along the true path satisfy the requirements of the construction.


Title: Standard and nonstandard models
Speaker:  Rumen Dimitrov, Western Illinois University
http://www.wiu.edu/users/rdd104/home.htm
Date and Time: Wednesday, February 19, 3:45PM-5:00PM
Place: Phillips Hall (801 22nd Street), Room 736
 

Abstract:  We will discuss the spectrum of standard and nonstandard models of arithmetic and of other systems of axioms. We will emphasize the importance of nonstandard models.


Title: On computable fields of reals and some applications
Speaker:  Victor Selivanov, Institute of Informatics Systems, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
https://persons.iis.nsk.su/en/vseliv
Date and Time: Friday, February 14, 12:30PM-1:30PM
Place: Phillips Hall (801 22nd Street), Room 736
 

Abstract:  In this joint work with Svetlana Selivanova we will discuss relationships of computably presentable ordered fields of reals with the field of computable reals. This have some applications to computable analysis, notably to linear algebra and to computing solutions of some linear systems of PDEs.


Title: On Sigma preorderings in HF(R)
Speaker: Andrei Morozov, Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
http://www.math.nsc.ru/%7Easm256/
Date and Time: Wednesday, February 12, 3:45PM-5:00PM
Place: Phillips Hall (801 22nd Street), Room 736
 

Abstract:  We prove that omega_1 cannot be embedded into any preordering Sigma-definable with parameters in the hereditarily finite superstructure over the ordered field of real numbers, HF(R).
As corollaries, we obtain characterizations of Sigma-presentable ordinals and Goedel constructive sets of kind L_alpha. It also follows that there are no Sigma-presentations for structures of Turing degrees and strong degrees, over HF(R).


 

 
 

 

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