Related papers: Completions of Kleene's second model

Exactly integrable systems connected to semisimple algebras of second rank with an arbitrary choice of grading are presented in explicit form. General solutions of these systems are expressed in terms of matrix elements of two fundamental…

We provide an extension of concurrent Kleene algebras to account for probabilistic properties. The algebra yields a unified framework containing nondeterminism, concurrency and probability and is sound with respect to the set of…

Many mathematical models have been leveraged to design embeddings for representing Knowledge Graph (KG) entities and relations for link prediction and many downstream tasks. These mathematically-inspired models are not only highly scalable…

We develop the theory of layered posets, and use the notion of layering to prove a new iteration theorem (Theorem 6): if $\kappa$ is weakly compact then any universal Kunen iteration of $\kappa$-cc posets (each possibly of size $\kappa$) is…

In this paper, we proposed an procedure to construct the completion of the integrable system by adding a perturbation to the generalized matrix problem, which can be used to continuous integrable couplings, discrete integrable couplings and…

Let K be an Abstract Elemenetary Class satisfying the amalgamation and the joint embedding property, let \mu be the Hanf number of K. Suppose K is tame. MAIN COROLLARY: (ZFC) If K is categorical in a successor cardinal bigger than…

In dimension two, we study complete monomial ideals combinatorially, their Rees algebras and develop effective means to find their defining equations.

Let $k$ be an algebraically closed field of prime characteristic $p$. Let $kGe$ be a block of a group algebra of a finite group $G$, with normal defect group $P$ and abelian $p'$ inertial quotient $L$. Then we show that $kGe$ is a matrix…

We analyze the intermediate models of the strongly compact Prikry forcing. We exhibit a simple combinatorial property which, for a given supercompact cardinal $\kappa$, characterize the projections of all projections of the strongly compact…

The probabilistic principal component analysis (PPCA) is built upon a global linear mapping, with which it is insufficient to model complex data variation. This paper proposes a mixture of bilateral-projection probabilistic principal…

We introduce the $N=2$ Lie conformal superalgebras ${\frak {K}}(p)$ of Block type, and classify their finite irreducible conformal modules for any nonzero parameter $p$. where $p$ is a nonzero complex number. In particular, we show that…

We study a class of extensions of the k-contracted Poincar\'e algebra under the hipotesis of generalizing the Bargmann algebra and his central charge. As we will see this type of contractions will lead in a natural way to consider the…

For a monadic sentence psi in the finite vocabulary we show that the spectra, the set of cardinalities of models of psi is almost periodic under reasonable conditions. The first is that every model is so called ``weakly k-decomposable''.…

We apply the recently developed technology of cofinality spectrum problems to prove a range of theorems in model theory. First, we prove that any model of Peano arithmetic is $\lambda$-saturated iff it has cofinality $\geq \lambda$ and the…

We give an elementary construction of the exact completion of a weakly lex category for categories enriched in the cartesian closed category $\mathsf{Pos}$ of partially ordered sets. Paralleling the ordinary case, we characterize categories…

Energy problems are important in the formal analysis of embedded or autonomous systems. Using recent results on star-continuous Kleene omega-algebras, we show here that energy problems can be solved by algebraic manipulations on the…

In this paper, we show that the equational theory of relational Kleene algebra with the \emph{graph loop} operator (a.k.a.~\emph{fixset}) is \textsc{PSpace}-complete. Here, the graph loop is the unary operator that restricts a binary…

We revisit the duality between Kripke and algebraic semantics of intuitionistic and intuitionistic modal logic. We find that there is a certain mismatch between the two semantics, which means that not all algebraic models can be embedded…

We present an easy construction producing a Kleene lattice K from an arbitrary distributive lattice L and a non-empty subset of L. We show that L can be embedded into K and compute the cardinality of K under certain additional assumptions.…

For I a proper, countably complete ideal on P(X) for some set X, can the quotient Boolean algebra P(X)/I be complete? This question was raised by Sikorski in 1949. By a simple projection argument as for measurable cardinals, it can be…