Non-equational stable groups.

Speaker: Rizos Sklinos

Abstract: The notion of equationality has been introduced by Srour and further

developed by Pillay-Srour. It is best understood intuitively as a notion

of Noetherianity on instances of first-order formulas. A first-order

theory is equational when every first-order formula is equivalent to a

boolean combination of equations.

Equationality implies stability and for many years these two notions were

identified, as only an "artificial" example of Hrushovski (a tweaked

pseudo-space) was witnessing otherwise. Recently Sela proved that the

theory of the free group is stable but not equational providing us with

the first natural example of a stable non-equational theory.

We give a transparent proof of the non-equationality of the free group and

we expand the result to the first-order theory of any nontrivial free

product which is not Z_2*Z_2.

In combination with Sela's deep result that the free product of stable

groups is still stable, our result gives an abundance of examples of new

stable non-equational theories.

This is a joint work with Isabel Müller.

Speaker: Rizos Sklinos

Abstract: The notion of equationality has been introduced by Srour and further

developed by Pillay-Srour. It is best understood intuitively as a notion

of Noetherianity on instances of first-order formulas. A first-order

theory is equational when every first-order formula is equivalent to a

boolean combination of equations.

Equationality implies stability and for many years these two notions were

identified, as only an "artificial" example of Hrushovski (a tweaked

pseudo-space) was witnessing otherwise. Recently Sela proved that the

theory of the free group is stable but not equational providing us with

the first natural example of a stable non-equational theory.

We give a transparent proof of the non-equationality of the free group and

we expand the result to the first-order theory of any nontrivial free

product which is not Z_2*Z_2.

In combination with Sela's deep result that the free product of stable

groups is still stable, our result gives an abundance of examples of new

stable non-equational theories.

This is a joint work with Isabel Müller.

## Date:

Wed, 15/03/2017 - 16:00 to 18:00

## Location:

Ross 70