Another related reference, is the following thesis: ``An Abstract Condensation Property'' by David Richard Law.

Here is the abstract of it:

Let $A = (A, ... )$ be a relational structure. Say that $A$ has condensation if there is an $F : A^{< ω} → A$ such that for every partial order $P$, it is forced by $P$ that substructures of $A$ which are closed under $F$ are isomorphic to elements of the ground model. Condensation holds if every structure in $V$, the universe of sets, has condensation. This property, isolated by Woodin, captures part of the content of the condensation lemmas for $L, K$ and other "$L$-like" models. We present a variety of results having to do with condensation in this abstract sense. Section 1 establishes the absoluteness of condensation and some of its consequences. In particular, we show that if condensation holds in $M$, then $M ╞ GCH$ and there are no measurable cardinals or precipitous ideals in $M$. The results of this section are due to Woodin. Section 2 contains a proof that condensation implies $◊_κ(E)$ for $κ$ regular and $E \subseteq κ$ stationary. This is the main result of this thesis. The argument provides a new proof of the key lemma giving $GCH$. Section 2 also contains some information about the relationship between condensation and strengthenings of diamond. Section 3 contains partial results having to do with forcing "Cond(A)", some further discussion of the relation between condensation and combinatorial principles which hold in $L$, and an argument that Cond(G) fails in $V[G]$, where $G$ is generic for the partial order adding $ω_2$ cohen subsets of $ω_1.$

Another related reference, is the following “An Abstract Condensation Property” by David Richard Law.

Here is the abstract of it:

Let $A = (A, \dotsc)$ be a relational structure. Say that $A$ has condensation if there is an $F : A^{< \omega} → A$ such that for every partial order $P$, it is forced by $P$ that substructures of $A$ which are closed under $F$ are isomorphic to elements of the ground model. Condensation holds if every structure in $V$, the universe of sets, has condensation. This property, isolated by Woodin, captures part of the content of the condensation lemmas for $L$, $K$ and other "$L$-like" models. We present a variety of results having to do with condensation in this abstract sense. Section 1 establishes the absoluteness of condensation and some of its consequences. In particular, we show that if condensation holds in $M$, then $M \models \mathrm{GCH}$ and there are no measurable cardinals or precipitous ideals in $M$. The results of this section are due to Woodin. Section 2 contains a proof that condensation implies $\Diamond_κ(E)$ for $\kappa$ regular and $E \subseteq \kappa$ stationary. This is the main result of this thesis. The argument provides a new proof of the key lemma giving GCH. Section 2 also contains some information about the relationship between condensation and strengthenings of diamond. Section 3 contains partial results having to do with forcing "$\operatorname{Cond}(A)$", some further discussion of the relation between condensation and combinatorial principles which hold in $L$, and an argument that $\operatorname{Cond}(G)$ fails in $V[G]$, where $G$ is generic for the partial order adding $\omega_2$ cohen subsets of $\omega_1$.

Another related reference, is the following thesis: ``An Abstract Condensation Property'' by David Richard Law.

Here is the abstract of it:

Let $A = (A, ... )$ be a relational structure. Say that $A$ has condensation if there is an $F : A^{< ω} → A$ such that for every partial order $P$, it is forced by $P$ that substructures of $P$ which are closed under $F$ are isomorphic to elements of the ground model. Condensation holds if every structure in $V$, the universe of sets, has condensation. This property, isolated by Woodin, captures part of the content of the condensation lemmas for $L, K$ and other "$L$-like" models. We present a variety of results having to do with condensation in this abstract sense. Section 1 establishes the absoluteness of condensation and some of its consequences. In particular, we show that if condensation holds in $M$, then $M ╞ GCH$ and there are no measurable cardinals or precipitous ideals in $M$. The results of this section are due to Woodin. Section 2 contains a proof that condensation implies $◊_κ(E)$ for $κ$ regular and $E \subseteq κ$ stationary. This is the main result of this thesis. The argument provides a new proof of the key lemma giving $GCH$. Section 2 also contains some information about the relationship between condensation and strengthenings of diamond. Section 3 contains partial results having to do with forcing "Cond(A)", some further discussion of the relation between condensation and combinatorial principles which hold in $L$, and an argument that Cond(G) fails in $V[G]$, where $G$ is generic for the partial order adding $ω_2$ cohen subsets of $ω_1.$

Another related reference, is the following thesis: ``An Abstract Condensation Property'' by David Richard Law.

Here is the abstract of it:

Let $A = (A, ... )$ be a relational structure. Say that $A$ has condensation if there is an $F : A^{< ω} → A$ such that for every partial order $P$, it is forced by $P$ that substructures of $A$ which are closed under $F$ are isomorphic to elements of the ground model. Condensation holds if every structure in $V$, the universe of sets, has condensation. This property, isolated by Woodin, captures part of the content of the condensation lemmas for $L, K$ and other "$L$-like" models. We present a variety of results having to do with condensation in this abstract sense. Section 1 establishes the absoluteness of condensation and some of its consequences. In particular, we show that if condensation holds in $M$, then $M ╞ GCH$ and there are no measurable cardinals or precipitous ideals in $M$. The results of this section are due to Woodin. Section 2 contains a proof that condensation implies $◊_κ(E)$ for $κ$ regular and $E \subseteq κ$ stationary. This is the main result of this thesis. The argument provides a new proof of the key lemma giving $GCH$. Section 2 also contains some information about the relationship between condensation and strengthenings of diamond. Section 3 contains partial results having to do with forcing "Cond(A)", some further discussion of the relation between condensation and combinatorial principles which hold in $L$, and an argument that Cond(G) fails in $V[G]$, where $G$ is generic for the partial order adding $ω_2$ cohen subsets of $ω_1.$