2012 seminar talk: On Sigma-definability of structures over the reals

Talk held by Andrey Morozov (Novosibirsk State University, Russia) at the KGRC seminar on 2012-06-28.

Abstract

We give a brief survey of the results on structures $\Sigma$-definable over $HF(R)$ and present some further results on the number of non-$\Sigma$-isomorphic presentations of the ordered field R of reals and of its ordering. In particular, we will discuss a question, whether is it possible to use R to 'improve' itself by creating its new classically isomorphic $\Sigma$-copy.