Added highlighting of defs

_posts/2024-11-26-understanding-godel-incompleteness-theorems.md

@@ -62,11 +62,11 @@ Counterreciprocal for example is based on the *modus tollens*, which is "a form
 
 ### Syntax and semantics
 
-In mathematics, when we talk about statements, rules of logic, and axioms, we are referring to elements that exist within the realm of **syntax**. Syntax is essentially the structure or the form of our mathematical language. It is about how we write and manipulate symbols to form proofs. Think of syntax as the grammar and rules of a language that allow us to construct meaningful sentences, or in this case, proofs. The syntax allow as to say $P \implies Q$ without saying what $P$ or $Q$ are and without stating if they are true or not, nor what that "implies" actually mean.
+In mathematics, when we talk about statements, rules of logic, and axioms, we are referring to elements that exist within the realm of **syntax**. <u>Syntax is essentially the structure or the form of our mathematical language</u>. It is about how we write and manipulate symbols to form proofs. Think of syntax as the grammar and rules of a language that allow us to construct meaningful sentences, or in this case, proofs. The syntax allow as to say $P \implies Q$ without saying what $P$ or $Q$ are and without stating if they are true or not, nor what that "implies" actually mean.
 
-On the other hand, **semantics** is about meaning and truth. It is concerned with what these syntactical structures actually represent in the real world or in any abstract model we choose. Semantics gives life to the syntax by assigning truth values to statements, determining whether they are true or false and what they actually represent. It is to concretize the abstraction of syntax. This is where models come into play.
+On the other hand, **semantics** is about meaning and truth. <u>It is concerned with what these syntactical structures actually represent in the real world or in any abstract model we choose</u>. Semantics gives life to the syntax by assigning truth values to statements, determining whether they are true or false and what they actually represent. It is to concretize the abstraction of syntax. This is where models come into play.
 
-**A model in semantics** is a specific interpretation of the symbols and statements in our language. It provides a concrete context in which we can evaluate the truth of statements. For example, in Boolean logic (the most common logic in mathematics), a model might assign the truth value 'true' or 'false' to each statement and also might say that the domain is the natural numbers (the objects we are reasoning about).
+**A model in semantics** is a <u>specific interpretation of the symbols and statements in our language</u>. It provides a concrete context in which we can evaluate the truth of statements. For example, in Boolean logic (the most common logic in mathematics), a model might assign the truth value 'true' or 'false' to each statement and also might say that the domain is the natural numbers (the objects we are reasoning about).
 
 > Syntax = proof = symbols = abstract
 >