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Seminar Details

The Finite Basis Problem

  • Start Date: May 26, 2008
  • Event Start Time: 12:00 PM
  • Event End Time: 1:00 PM
  • Organizers: Christine Agnese
  • Seminar Series: REU Seminar
  • Presenter(s): Simon Thomas - Rutgers University
  • Event Location: DIMACS Seminar room
  • Abstract: Let C be a class of structures. (For example, C could be the class of countably infinite graphs.) Then a basis for C is a collection B ⊆ C such that for each C ∈ C, there exists B ∈ B such that B embeds into C. The Finite Basis Problem asks whether C has a finite basis. In this talk, we shall begin by solving the Finite Basis Problem for the cases when: • C = the class of countably infinite graphs; • C = the class of countably infinite linear orders; • C = the class of countably infinite partial orders; • C = the class of countably infinite groups. Then we shall consider the more challenging cases when C is the class of uncountable graphs or uncountable linear orders.