COMPLETE ADDITIVITY AND MODAL INCOMPLETENESS

Complete Additivity and Modal Incompleteness

Market Incompleteness and Super Value Additivity: Implications for Securitization∗

In an incomplete market economy, all claim cannot be priced uniquely based on arbitrage. The prices of attainable claims (those that are spanned by traded claims) can be determined uniquely, whereas the prices of those that are unattainable can only be bounded. We first show that tighter price bounds can be determined by considering all possible portfolios of unattainable claims for which there...

An Intuitively Complete Analysis of Godel's Incompleteness

A detailed and rigorous analysis of Gödel’s proof of his first incompleteness theorem is presented. The purpose of this analysis is two-fold. The first is to reveal what Gödel actually proved to provide a clear and solid foundation upon which to base future research. The second is to construct a coherent explication of Gödel’s proof that is not only approachable by the non-specialist, but also ...

An Algebraic Approach to Incompleteness in Modal Logic by

1 Acknowledgments I would like to thank heartily: • Professor Hiroakira Ono, the principal advisor of this thesis. His decision to accept an almost completely unknown foreigner as a PhD student was risky and brave. I can only hope he did not regret it at times. It would be impossible to write this thesis, live and study in Japan without his support. Special thanks for allowing and encouraging m...

Contents 1 On the Incompleteness of Modal Logics