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Fraïssé limit via forcing | ||
| Journal of Mahani Mathematical Research | ||
| دوره 13، شماره 4 - شماره پیاپی 29، اسفند 2024، صفحه 21-25 اصل مقاله (438.67 K) | ||
| نوع مقاله: Special Issue Dedicated to Prof. Esfandiar Eslami | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2024.22473.1535 | ||
| نویسنده | ||
| Mohammad Golshani* | ||
| School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran-Iran. | ||
| چکیده | ||
| 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 a Fra\"{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 a Fra\"{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. | ||
| کلیدواژه‌ها | ||
| Fraisse limit؛ Focing؛ uncountable cardinals | ||
| مراجع | ||
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[1] Ackerman, Nathanael; Golshani, Mohammad; Mirabi, Mostafa; Cohen Generic Structures with Functions, preprint,
[2] Hodges, Wilfrid Model theory. Encyclopedia of Mathematics and its Applications, 42. Cambridge University Press, Cambridge, 1993. xiv+772 pp. ISBN: 0-521-30442-3
[3] Kostana, Ziemowit; Forcing-theoretic framework for the Frasse theory, PhD thesis.
[4] Kostana, Ziemowit; Cohen-like rst order structures, Ann. Pure Appl. Logic174(2023), no.1, Paper No. 103172, 17 pp. | ||
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