Pseudo-Exponential Structures and Exponential Algebraic Closedness in the Surreal Numbers

Key Points

• The aim is to explore a pseudo-exponential model in surreal numbers and prove its structural advantages over real and complex numbers.
• Developed a pseudo-exponential model for surreal numbers
• Proposed methodology for solving P(x,e^x) = 0 in surreal numbers
• Provided a formal proof of stronger exponential-algebraic closedness in surreal numbers
• Introduced an axiomatic scheme for surreal numbers involving Hahn geometry
• Demonstrated the pseudo-exponential model addresses equation-solving effectively in surreal numbers
• Established that exponential-algebraic closedness in surreal numbers is more robust than in real and complex numbers
• Proposed axioms that integrate concepts of surreal rotundity and support freeness