Fraïssé limit via forcing
Suppose $\mathcal{L}$ is a finite relational language and $\mathcal{K}$ is a class of finite $\mathcal{L}$-structures closed under substructures and isomorphisms. It is called aFra\"{i}ss\'{e} class if it satisfies Joint Embedding Property (JEP) and Amalgamation Property (AP). A Fra\"...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Shahid Bahonar University of Kerman
2024-12-01
|
| Series: | Journal of Mahani Mathematical Research |
| Subjects: | |
| Online Access: | https://jmmrc.uk.ac.ir/article_4112_f817a30f4eb6c933680a5926059f0e3e.pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1841560204270895104 |
|---|---|
| author | Mohammad Golshani |
| author_facet | Mohammad Golshani |
| author_sort | Mohammad Golshani |
| collection | DOAJ |
| description | Suppose $\mathcal{L}$ is a finite relational language and $\mathcal{K}$ is a class of finite $\mathcal{L}$-structures closed under substructures and isomorphisms. It is called aFra\"{i}ss\'{e} class if it satisfies Joint Embedding Property (JEP) and Amalgamation Property (AP). A Fra\"{i}ss\'{e} limit, denoted $Flim(\mathcal{K})$, of aFra\"{i}ss\'{e} class $\mathcal{K}$ is the unique\footnote{The existence and uniqueness follows from Fra\"{i}ss\'{e}'s theorem, See \cite{hodges}.} countable ultrahomogeneous (every isomorphism of finitely-generated substructures extends to an automorphism of $Flim(\mathcal{K})$) structure into which every member of $\mathcal{K}$ embeds.Given a Fraïssé class K and an infinite cardinal κ, we define a forcing notion which adds a structure of size κ using elements of K, which extends the Fraïssé construction in the case κ=ω. |
| format | Article |
| id | doaj-art-a1c6fef620544d56bf588e3cb2ea3abd |
| institution | Kabale University |
| issn | 2251-7952 2645-4505 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Shahid Bahonar University of Kerman |
| record_format | Article |
| series | Journal of Mahani Mathematical Research |
| spelling | doaj-art-a1c6fef620544d56bf588e3cb2ea3abd2025-01-04T19:29:49ZengShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-79522645-45052024-12-01134212510.22103/jmmr.2024.22473.15354112Fraïssé limit via forcingMohammad Golshani0School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran-Iran.Suppose $\mathcal{L}$ is a finite relational language and $\mathcal{K}$ is a class of finite $\mathcal{L}$-structures closed under substructures and isomorphisms. It is called aFra\"{i}ss\'{e} class if it satisfies Joint Embedding Property (JEP) and Amalgamation Property (AP). A Fra\"{i}ss\'{e} limit, denoted $Flim(\mathcal{K})$, of aFra\"{i}ss\'{e} class $\mathcal{K}$ is the unique\footnote{The existence and uniqueness follows from Fra\"{i}ss\'{e}'s theorem, See \cite{hodges}.} countable ultrahomogeneous (every isomorphism of finitely-generated substructures extends to an automorphism of $Flim(\mathcal{K})$) structure into which every member of $\mathcal{K}$ embeds.Given a Fraïssé class K and an infinite cardinal κ, we define a forcing notion which adds a structure of size κ using elements of K, which extends the Fraïssé construction in the case κ=ω.https://jmmrc.uk.ac.ir/article_4112_f817a30f4eb6c933680a5926059f0e3e.pdffraisse limitfocinguncountable cardinals |
| spellingShingle | Mohammad Golshani Fraïssé limit via forcing Journal of Mahani Mathematical Research fraisse limit focing uncountable cardinals |
| title | Fraïssé limit via forcing |
| title_full | Fraïssé limit via forcing |
| title_fullStr | Fraïssé limit via forcing |
| title_full_unstemmed | Fraïssé limit via forcing |
| title_short | Fraïssé limit via forcing |
| title_sort | fraisse limit via forcing |
| topic | fraisse limit focing uncountable cardinals |
| url | https://jmmrc.uk.ac.ir/article_4112_f817a30f4eb6c933680a5926059f0e3e.pdf |
| work_keys_str_mv | AT mohammadgolshani fraisselimitviaforcing |