Related papers: Set-Theoretic Blockchains
Let $B_n$ be the poset generated by the subsets of $[n]$ with the inclusion as relation and let $P$ be a finite poset. We want to embed $P$ into $B_n$ as many times as possible such that the subsets in different copies are incomparable. The…
We present a categorical theory of the composition methods in finite model theory -- a key technique enabling modular reasoning about complex structures by building them out of simpler components. The crucial results required by the…
Using forcing with measured creatures we build a universe of set theory in which: (a) every sup-measurable function f:RxR-->R is measurable, and (b) every function f:R-->R is continuous on a non-measurable set. This answers a question of…
A theoretical development is carried to establish fundamental results about rank-initial embeddings and automorphisms of countable non-standard models of set theory, with a keen eye for their sets of fixed points. These results are then…
A few steps are made towards representation theory of embeddability among uncountable graphs. A monotone class of graphs is defined by forbidding countable subgraphs, related to the graph's end-structure. Using a combinatorial theorem of…
The blockchain trilemma highlights the difficulty of simultaneously achieving a high degree of decentralization (DoD), scalability, and security in blockchain systems. While numerous constructs and metrics have been proposed to analyze…
Blockchain is one of the most popular topics for discussion now. However, most experts still see this technology as only part of Bitcoin, other crypto-currencies or money transfer systems. Often, new solutions, proposed by young…
Quantum blockchains provide inherent resilience against quantum adversaries and represent a promising alternative to classical blockchain systems in the quantum era. However, existing quantum blockchain architectures largely depend on…
Trust models are essential components of networks of any nature, as they refer to confidence frameworks to evaluate and verify if their participants act reliably and fairly. They are necessary to any social, organizational, or computer…
We introduce notions of combinatorial blowups, building sets, and nested sets for arbitrary meet-semilattices. This gives a common abstract framework for the incidence combinatorics occurring in the context of De Concini-Procesi models of…
Graph embeddings are low dimensional representations of nodes, edges or whole graphs. Such representations allow for data in a network format to be used along with machine learning models for a variety of tasks (e.g., node classification),…
The technique of "classical realizability" is an extension of the method of "forcing"; it permits to extend the Curry-Howard correspondence between proofs and programs, to Zermelo-Fraenkel set theory and to build new models of ZF, called…
This is an overview about a method of constructing ccc forcings: Suppose first that a continuous, commutative system of complete embeddings between countable forcings indexed along $\omega_1$ is given. Then its direct limit satisfies ccc by…
With the advancement of blockchain systems, many recent research works have proposed distributed ledger technology~(DLT) that employs Byzantine fault-tolerant~(BFT) consensus protocols to decide which block to append next to the ledger.…
In recent years, the term Metaverse emerged as one of the most compelling concepts, captivating the interest of international companies such as Tencent, ByteDance, Microsoft, and Facebook. These company recognized the Metaverse as a pivotal…
We develop a general framework (multidimensional asymptotic classes, or m.a.c.s) for handling classes of finite first order structures with a strong uniformity condition on cardinalities of definable sets: The condition asserts that…
Blockchain systems come with a promise of decentralization that often stumbles on a roadblock when key decisions about modifying the software codebase need to be made. This is attested by the fact that both of the two major…
We study Medvedev reducibility in the context of set theory -- specifically, forcing and large cardinal hypotheses. Answering a question of Hamkins and Li \cite{HaLi}, we show that the Medvedev degrees of countable ordinals are far from…
Decentralization is a fundamental design element of the Web3 economy. Blockchains and distributed consensus mechanisms are touted as fault-tolerant, attack-resistant, and collusion-proof because they are decentralized. Recent analyses,…
In a blockchain system, nodes regularly distribute data to other nodes. The ideal perspective taken in the scientific literature is that data is broadcast to all nodes directly, while in practice data is distributed by repeated multicast.…