Godelian Semantic Embeddings

We introduce a semantic embedding strategy that allows 2 conditional statements defined in FOA to create a semantic fixed point that implies Godelian G. We use this to show that we can derive the ordinal hierarchy without the use of the Axiom of Infinity. We replicate this ordinal construction finding via diagonalization in "negation space" showing its expressiveness. We then apply this semantic embedding strategy to Hilbert space, creating a semantic Hilbert space composed of representational and negation subspaces. We then demonstrate that mathematical undecidability and physical indeterminacy have logically isometry in the semantic Hilbert space model. We then examine several noteworthy mathematical problems including RH, BSD, Hodge, YM, NS, P vs. NP, and CH, showing that they can be understood within this interpretative model, creating several new perspectives on how to understand their potential solutions. String theory is shown to have the model of this semantic Hilbert space and recommendations are made for how semantic embeddings can be applied to the Langlands program. Applications of a semantic Hilbert model to the black hole paradox and quantum vacuum are explored.