Related papers: Set-Theoretic Blockchains
Generic absoluteness is the phenomenon that certain truths in the set-theoretic universe remain stable under forcing expansions. A classical result by Kripke asserts that every complete Boolean algebra completely embeds into a countably…
Blockchain has many benefits including decentralization, availability, persistency, consistency, anonymity, auditability and accountability, and it also covers a wide spectrum of applications ranging from cryptocurrency, financial services,…
This paper argues that mathematical objects are constructions and that constructions introduce a flexibility in the ways that mathematical objects are represented (as sets of binary sequences for example) and presented (in a particular…
In this sequel to my previous paper, "Is String Theory in Knots?" I explore ways of constructing symmetries through an algebraic stepping process using knotted graphs. The hope is that this may lead to an algebraic formulation of string…
A comparative study across the most widely known blockchain technologies is conducted with a bottom-up approach. Blockchains are disentangled into building blocks. Each building block is then hierarchically classified in main and…
In the past decade, blockchain has shown a promising vision greatly to build the trust without any powerful third party in a secure, decentralized and salable manner. However, due to the wide application and future development from…
Metaverse has rekindled human beings' desire to further break space-time barriers by fusing the virtual and real worlds. However, security and privacy threats hinder us from building a utopia. A metaverse embraces various techniques, while…
Blockchain is a radical innovation with a unique value proposition that shifts trust from institutions to algorithms. Still, the potential of blockchains remains elusive due to knowledge gaps between computer science research and…
A central theme in set theory is to find universes with extreme, well-understood behaviour. The case we are interested in is assuming GCH and has a strong forcing axiom of higher order than usual. Instead of "for every suitable forcing…
This paper presents Thinkey, an efficient, secure, infinitely scalable and decentralized blockchain architecture. It ensures system correctness and liveness by a multi-layer structure. In particular, the system is based on a double-chain…
The structures $\langle M,\subseteq^M\rangle$ arising as the inclusion relation of a countable model of sufficient set theory $\langle M,\in^M\rangle$, whether well-founded or not, are all isomorphic. These structures $\langle…
The explosive advent of the blockchain technology has led to hundreds of blockchain systems in the industry, thousands of academic papers published over the last few years, and an even larger number of new initiatives and projects. Despite…
Blockchain technology and related frameworks have recently received extensive attention. Blockchain systems use multi-party consensus protocols to reach agreements on transactions. Hyperledger Fabric framework exposes a multi-party…
The multiverse view in set theory, introduced and argued for in this article, is the view that there are many distinct concepts of set, each instantiated in a corresponding set-theoretic universe. The universe view, in contrast, asserts…
Blockchain consensus is a state whereby each node in a network agrees on the current state of the blockchain. Existing protocols achieve consensus via a contest or voting procedure to select one node as a dictator to propose new blocks.…
We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already,…
We consider partially ordered sets of combinatorial structures under consecutive orders, meaning that two structures are related when one embeds in the other such that `consecutive' elements remain consecutive in the image. Given such a…
Every mathematical structure has an elementary extension to a pseudo-countable structure, one that is seen as countable inside a suitable class model of set theory, even though it may actually be uncountable. This observation, proved easily…
In previous papers on this project a general static logical framework for formalizing and mechanizing set theories of different strength was suggested, and the power of some predicatively acceptable theories in that framework was explored.…
Blockchain, also coined as decentralized AI, has the potential to empower AI to be more trustworthy by creating a decentralized trust of privacy, security, and audibility. However, systematic studies on the design principle of blockchain as…