Timeline for Boolean rings with many automorphisms
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 23 at 11:02 | comment | added | YCor | Still another one: inside the Boolean algebra of finite Boolean combinations of intervals of the real line, pick the bounded ones (this is an ideal) and mod out by the smaller ideal of finite subsets. | |
| Oct 23 at 9:51 | comment | added | Emil Jeřábek | Boolean algebras where all elements $\ne0,1$ are in the same orbit are called homogeneous in forcing literature, which is replete with such examples. In fact, set theorists strongly prefer homogeneous forcings, because then the validity of statements in the generic extension $V[G]$ does not depend on the choice of the generic filter; if the forcing is not homogeneous, you’d better decompose it to pieces that are. | |
| Oct 23 at 6:56 | answer | added | John Griesmer | timeline score: 1 | |
| Oct 21 at 13:07 | comment | added | YCor | Actually this is almost the same as asking about unital BAs $A$ in which the automorphism group has exactly 3 orbits: $\{0\}$, $\{1\}$ and the remainder. Which in Stone duality means Stone space in which all proper nonempty clopen subsets are equivalent modulo homeomorphism. Given such $A$, the kernel of every homomorphism to $\mathbf{Z}/2\mathbf{Z}$ provides an example of a non-unital BA with two orbits under automorphisms ($\{0\}$ and the remainder). | |
| Oct 21 at 7:20 | history | became hot network question | |||
| Oct 21 at 5:12 | answer | added | David Gao | timeline score: 5 | |
| Oct 21 at 3:48 | answer | added | YCor | timeline score: 7 | |
| Oct 20 at 23:35 | comment | added | Noah Schweber | Let $\mathcal{R}$ be the subring of $\mathcal{P}(\omega)/\mathit{Fin}$ consisting of (classes containing) sets of asymptotic density zero. Does this work? | |
| Oct 20 at 23:20 | history | asked | Greg Oman | CC BY-SA 4.0 |