adoptions more

adoptions/intro.tex

@@ -80,11 +80,10 @@ introduced realms \cite{CarFarKoh:rsckmt14}.
 
 In Section~\ref{sec:pheno} we briefly review the structure of mathematical documents and
 build our intuitions about ``recaps'' by looking at some examples.  We discuss how to
-represent them using theory graphs in section \ref{sec:patterns}. Section~\ref{sec:conc}
+represent them using theory graphs in Section \ref{sec:patterns}. Section~\ref{sec:conc}
 concludes the paper and discusses future work.
 
 
-
 %%% Local Variables:
 %%% mode: latex
 %%% TeX-master: "paper"

adoptions/patterns.tex

-In this section we look more closely at the examples from section \ref{sec:pheno} and how
+In this section we look more closely at the examples from Section \ref{sec:pheno} and how
 each can be represented using theory graphs.  But first, we look at the aspects common to
 all examples to form an intuition of the theory graphs structures that are needed.
 
-The examples in section \ref{sec:pheno} are each slightly different but they have
+The examples in Section \ref{sec:pheno} are each slightly different but they have
 fundamental common aspects.  First, each paper starts with establishing a common ground on
 which the results of the paper are built. This leverages the literature in two ways.
 \begin{itemize}
@@ -355,7 +355,7 @@ sample papers we studied.
 Note that adding an equivalent definition corresponds to a \textbf{realm extension}, where
 the face is fixed, and the view from the face to the current theory can be
 postulated. Therefore, in Figure \ref{fig:rec-mnets} the paper effectively extends the
-realm (or the current pillar) as introduced in section \ref{sec:prel-realms}.  This
+realm (or the current pillar) as introduced in Section \ref{sec:prel-realms}.  This
 corresponds to the mathematical practice of ``contributing to'' a field (or mathematical
 theory). This resulting realm after knowledge aggregation is shown in Figure
 \ref{fig:rec-mnets-aggr}, where the new paper contributes a new pillar to the realm. The
@@ -493,7 +493,7 @@ realm.
 
 \subsection{Postulated Recap/Adoption}\label{rc:ge}
 
-Finally, we have the case for educational material such as the one in example \ref{ex:course} where $r$ cannot be directly modeled
+Finally, we have the case for educational material such as the one in Example \ref{ex:course} where $r$ cannot be directly modeled
 as either an include or a view. This is caused by the constraint of self-containedness of such materials. Normally,
 in the case where a more formal development is used we could represent it as an include and be in the case for plain recaps. 
 However, the home theory of the new symbols must be the current development in order for it to be self-contained, so we cannot use an include. 

adoptions/phenomena.tex

@@ -72,7 +72,7 @@ notations. We show two examples where the mathematics involved is relatively ele
 
 \begin{example}\label{ex:covers}
   \cite{covers-orig} discusses covers of the multiplicative group of an algebraically
-  closed field which are formally defined in the beginning of the paper as follows:
+  closed field which are formally introduced in the beginning of the paper as follows:
   \begin{labeledquote}\sf
     \textbf{Definition 1.1} Let $V$ be a vector space over $Q$ and let $F$ be an
     algebraically closed field of characteristic $0$. A \emph{cover of the multiplicative
@@ -81,11 +81,11 @@ notations. We show two examples where the mathematics involved is relatively ele
     homomorphism from $(V, +)$ onto $(F^∗, \cdot)$ with kernel $K$. We will call this map
     \emph{exp}.
 \end{labeledquote}
-This just imports the terminology and definitions from an earlier paper.  However, when
-establishing results, \cite{covers-orig} mentions ``\textsf{Moreover, with an additional
-  axiom (in $L_{\omega_1\omega}$) stating $K \cong Z$, the class is categorical in
-  uncountable cardinalities. This was originally proved in [13] but an error was later
-  found in the proof and corrected in [2]}''.
+However, later, the authors source the concept origin to an earlier paper (``\textsf[13]'') and effectively import the terminology, 
+definitions and theorems. For instance, when establishing results, \cite{covers-orig} mentions 
+``\textsf{Moreover, with an additional axiom (in $L_{\omega_1\omega}$) stating $K \cong Z$, the 
+  class is categorical in uncountable cardinalities. This was originally proved in [13] but an error was later
+  found in the proof and corrected in [2].  Throughout this article, we will make the assumption $K \cong Z$.}''.
 % However, \cite{covers-orig} uses a
 % generalization of the concept in \cite{covers-13} which uses the sequence
 % $0 \arr Z \arr C \arr C^* \arr 1$ instead (although later proves some