|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'501'711
Articles rated: 2609
20 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Properly ergodic structures | | Nathanael Ackerman
; Cameron Freer
; Alex Kruckman
; Rehana Patel
; | | Date: |
25 Oct 2017 | | Abstract: | We consider ergodic $mathrm{Sym}(mathbb{N})$-invariant probability measures
on the space of $L$-structures with domain $mathbb{N}$ (for $L$ a countable
relational language), and call such a measure a properly ergodic structure when
no isomorphism class of structures is assigned measure $1$. We characterize
those theories in countable fragments of $mathcal{L}_{omega_1, omega}$ for
which there is a properly ergodic structure concentrated on the models of the
theory. We show that for a countable fragment $F$ of $mathcal{L}_{omega_1,
omega}$ the almost-sure $F$-theory of a properly ergodic structure has
continuum-many models (an analogue of Vaught’s Conjecture in this context), but
its full almost-sure $mathcal{L}_{omega_1, omega}$-theory has no models. We
also show that, for an $F$-theory $T$, if there is some properly ergodic
structure that concentrates on the class of models of $T$, then there are
continuum-many such properly ergodic structures. | | Source: | arXiv, 1710.9336 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER