Hey professor -- if you could include definitions in future videos, I think it would make these videos more usable for self-study :) So a relational structure \( C = (c, \{ \gamma_i : i \in I \} ) \) is a set \( c \) and set of relations \( \{ \gamma_i : i \in I \} \) on \( c \), and a substructure \( D = (d, \{ \delta_j : j \in J \} ) \) is just a subset \( d \subseteq c \) and set of relations \( \{ \delta_j : j \in J \} \subseteq \{ \gamma_i : i \in I \} \) on \( d \) ? When I embed \( A \) into \( C \), I inject \( a \overset{f}{\hookrightarrow} c \) such that \( \{ f(\alpha_k) : k \in K \} \subseteq \{ \gamma_i : i \in I \} \) ?
Hey professor -- if you could include definitions in future videos, I think it would make these videos more usable for self-study :)
So a relational structure \( C = (c, \{ \gamma_i : i \in I \} ) \) is a set \( c \) and set of relations \( \{ \gamma_i : i \in I \} \) on \( c \), and a substructure \( D = (d, \{ \delta_j : j \in J \} ) \) is just a subset \( d \subseteq c \) and set of relations \( \{ \delta_j : j \in J \} \subseteq \{ \gamma_i : i \in I \} \) on \( d \) ?
When I embed \( A \) into \( C \), I inject \( a \overset{f}{\hookrightarrow} c \) such that \( \{ f(\alpha_k) : k \in K \} \subseteq \{ \gamma_i : i \in I \} \) ?
Hi! There are videos earlier in the playlist "Introduction to mathematical logic" which properly introduce structures and embeddings.