Esther Elbaz (Paris): Grothendick ring of pairing function with no cycles
Thursday, 28.06.2018 11:00 im Raum SR 1D
If $p$ is a bijection between a set $M$ and $M^2$, we say that it is a
pairing function with no cycles if for any term $t(x_1,..., x_n)$
formed with $p$, and that is not a variable, we have, for every
$a_1,\ldots, a_n \in M$, $t(a1,\ldots, a_n) \neq a_1$.
The theory of pairing function with no cycles is the simplest example
of a stable theory that is not a limit of super stable theories. It has been studied by several authors and, in particular, it has been shown that it is complete and admits quantifier elimintation in a natural language.
Grothendieck rings of a structure have been introduced in Model Theory in 2000. Its construction relies on indentifying definable sets that are in definable bijection and generalizes the definition of
Grothendieck ring already known in algebraic geometry.
We will first give a brief survey of this model theoretic notion. Then
we'll compute the Grothendieck ring of pairing function with no
cycles, and show that it is isomorphic to $\mathbb{Z}[x]/(X-X^2)$.
Angelegt am 21.06.2018 von Martina Pfeifer
Geändert am 21.06.2018 von Martina Pfeifer
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