# Dan Teng: Semiautomatic Structures

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 19 November 2014, 17:00 hrs

Room: S17#04-04, Department of Mathematics, NUS

Speaker: Dan Teng

Title: Semiautomatic Structures

URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html

Semiautomatic structures generalise automatic structures in the sense
that for some of the relations and functions in the structure one only
requires the derived relations and structures are automatic when all
but one input are filled with constants. One can also permit that this
applies to equality in the structure so that only the sets of
representatives equal to a given element of the structure are regular
while equality itself is not an automatic relation on the domain of
representatives. It is shown that one can find semiautomatic
representations for the field of rationals and also for finite
algebraic field extensions of it. Furthermore, it is shown that there
are semiautomatic ordered rings consisting of the integers augmented
by the multiples of the square-root of a non-square integer; here the
order is the same as the corresponding order on the real numbers.