Timeline for O-minimality and forcing
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 5, 2021 at 10:49 | comment | added | Mohammad Golshani | @AndrésVillaveces The paper is now available Combinatorial and number-theoretic properties of generic reals. | |
| Nov 11, 2018 at 17:00 | comment | added | Danielle Ulrich | Does the formula $\phi(x) := \forall y \in C (x+y \in C)$ define the ground reals? (This doesn't have direct bearing on the question, but came up as I was playing around with it) | |
| Nov 11, 2018 at 14:08 | comment | added | Andrés Villaveces | (2) seems suspiciously straightforward. In some sense, adding $r\subset {\mathbb N}$ as a predicate you are adding something "very similar" to $\mathbb N$ or $\mathbb Z$ (but then (3) seems strange - what kind of generic extension gives (3)?) --- Now, for the Question: The set C of all Cohen reals is comeager in the new reals. My quick guess would be that some careful use of genericity implies non-definability of $\mathbb Z$. | |
| Nov 11, 2018 at 1:34 | comment | added | Mohammad Golshani | @NoahSchweberN Yes, that is essentially what I had in mind, o-minimality is preserved by adding constants | |
| Nov 10, 2018 at 16:08 | comment | added | Noah Schweber | Isn't (1) trivial? Naming an element can't change o-minimality since o-minimality refers to definitions with parameters. | |
| Nov 10, 2018 at 4:33 | history | asked | Mohammad Golshani | CC BY-SA 4.0 |