I'm a fourth-year computer science major at the University of Washington. My interests span several theoretical and applied disciplines, including computational complexity theory, logic and programming languages, and formal methods.

I am currently a teaching assistant for CSE 421: Introduction to Algorithms at the University of Washington.

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Theorem (Law of the Excluded Middle, Model Theoretic Version). For any predicate $A$ and structure $M$ on a language $\mathcal{L}$, $$M \vDash (A(x) \lor \neg A(x))$$

Proof. Let $s$ be a variable assignment. Note that $|M| = A^M \cup (|M| - A^M)$, $A$ is modelled by some subset of $|M|$. Suppose we have $\text{Val}_s^M(x) = x_s^M$ ($x$ is interpreted as $x_s^M$ in the meta-language). Then there are two cases:

1. $x_s^M \in A^M$. By definition, we have that $M,s \vDash A(x)$.
2. $x_s^M \in |M| - A^M$. Then, $x_s^M \notin A^M$, and so we have $M, s \nvDash A(x)$. By definition, $M,s \vDash \neg A(x)$.

So it is the case that $M, s \vDash (A(x) \lor \neg A(x))$. Since $s$ was arbitrary, we may disregard it, giving us the claim. $\qquad \square$