17 problems

Kim's pseudolinearity conjecture for minimal types
arXiv@arxiv
Kim's pseudolinearity conjecture. Every minimal type is either linear, or not even $k$ -linear for any $k$ .
Conjectureopengeometric-stability model-theory simple-theories
0
The stable forking conjecture
arXiv@arxiv
Stable forking conjecture. In a simple theory $T$ , forking is explained by the stable part of $T$ .
Conjectureopenmodel-theory simple-theories stable-theories
0
The equivalence of K(n)-simplicity and (n+2)-complete amalgamation
arXiv@arxiv
Let $T$ be a simple theory, let $K(n)$ -simplicity denote the corresponding simplicity property, and let $(n+2)$ -CA mean $(n+2)$ -complete amalgamation over any set. For $n>2$ , these…
Conjectureopenamalgamation model-theory simple-theories
1
The stable-witness characterization of forking
arXiv@arxiv
Let $T$ be a simple theory, and let two elements fork. A relation has the independence property if it witnesses the independence property. Stable-witness conjecture. If two element…
Conjectureopenforking independence-property simple-theories
1
The non-intertwining characterization of simplicity
arXiv@arxiv
Let $T$ be a theory without the strict order property. Say that a relation witnesses the independence property if it has the independence property, and say that a relation witnesse…
Conjectureopenforking independence-property simple-theories
0
Conjecture that forking dependence over every base is stable
arXiv@arxiv
Stability of the forking relation over a base. The dependence relation $x \mathrel{\mathop{\mathpalette\notind{}}_{C}} y$ over every base $C$ is stable: there is no $C$ -indiscernib…
Conjectureopenforking-independence model-theory simple-theories
0
The stable forking conjecture over a base
arXiv@arxiv
Stable forking conjecture over a base. If $a \mathrel{\mathop{\mathpalette\notind{}}_{C}} b$ , there is a formula $\varphi(x,b)\in\operatorname{tp}(a/Cb)$ which forks over $C$ , such…
Conjectureopenforking-independence model-theory simple-theories
1
The stable forking conjecture
arXiv@arxiv
Stable forking conjecture. If $a \mathrel{\mathop{\mathpalette\notind{}}_{C}} b$ , then there is a formula $\varphi(x,\overline{b})\in\operatorname{tp}(a/Cb)$ such that…
Conjectureopenforking-independence model-theory simple-theories
0
Koponen's supersimplicity conjecture for finite relational languages
arXiv@arxiv
Koponen's conjecture. Every simple theory with quantifier elimination in a finite relational language is supersimple.
Conjecturesolvedmodel-theory simple-theories supersimplicity
0
The stable forking conjecture
arXiv@arxiv
Stable forking conjecture. If $p(x)$ forks over $A$ , then some stable formula belonging to $p$ forks over $A$ .
Conjecturerefutedforking model-theory simple-theories
0
Tsuboi's simple-completion conjecture for fusions
arXiv@arxiv
Let $L_1$ and $L_2$ be languages with $L_1\cap L_2=\emptyset$ , and let $T_1$ and $T_2$ be theories in these languages. Let $T_\cup$ be their fusion in the combined language. Tsuboi…
Conjectureopenfusions model-theory simple-theories
0
The bounded PAC conjecture for infinite simple fields
arXiv@arxiv
A field is bounded if it has only finitely many extensions of each given finite degree, and it is PAC if every geometrically irreducible variety over it has a rational point. Bound…
Conjectureopenfield-arithmetic pseudo-algebraically-closed-fields simple-theories
0
The simple fields conjecture
arXiv@arxiv
Let $K$ be an infinite (super)-simple field. The simple fields conjecture. $K$ is a (perfect) PAC field. Duret showed that this conjecture implies the stable fields conjecture, but…
Conjectureopenmodel-theory pac-fields simple-theories
1
Independence characterization for sufficient reducts
arXiv@arxiv
Independence characterization conjecture. Then
Conjecturerefutedindependence model-theory simple-theories
1
Elimination of hyperimaginaries for simple theories
arXiv@arxiv
Conjecture on simple theories. Every simple theory eliminates hyperimaginaries.
Conjecturerefutedhyperimaginaries model-theory simple-theories
0
The stable forking conjecture for simple theories
arXiv@arxiv
Let $T$ be a complete theory in a language $L$ , and let $\mathfrak{C}$ be its monster model. A formula $\varphi(x,y)$ , for disjoint tuples of variables $x$ and $y$ , is stable if th…
Conjectureopenforking model-theory simple-theories
0
Lascar strong types coincide with strong types in simple theories
arXiv@arxiv
Lascar–strong-type conjecture. In every simple theory, Lascar strong types over $A$ coincide with strong types over $A$ .
Conjecturesolvedmodel-theory simple-theories types
0