Related papers: Unified First Law and Some Comments
In this paper, we investigate how the initial models and the final models for the polynomial functors can be uniformly specified in matching logic.
We show that an elementary proof of Fermat's Last Theorem (FLT) exists. Our paper also extends the scope of FLT from integers to all rational numbers.
This paper has been withdrawn by the author [arXiv admin].
Despite its apparent complexity, our world seems to be governed by simple laws of physics. This volume provides a philosophical introduction to such laws. I explain how they are connected to some of the central issues in philosophy, such as…
Most of the assertions in the theory of well ordered sets are quite simple. However, one of its central statements, Zermelo's theorem, stands out of this rule, for its well-known proofs are rather complicated. The aim of the current paper…
This paper looks at a common law legal system as a learning algorithm, models specific features of legal proceedings, and asks whether this system learns efficiently. A particular feature of our model is explicitly viewing various aspects…
A universal First-Letter Law (FLL) is derived and described. It predicts the percentages of first letters for words in novels. The FLL is akin to Benford's law (BL) of first digits, which predicts the percentages of first digits in a data…
An application of Levy's continuity theorem and Hankel transform allow us to establish a law limit theorem for the sequence $V_n=f(U)\sin(n U)$, where $U$ is uniformly distributed in $(0,1)$ and $f$ a given function. Further, we investigate…
Using a recently introduced algebraic framework for the classification of fragments of first-order logic, we study the complexity of the satisfiability problem for several ordered fragments of first-order logic, which are obtained from the…
The purpose of this note is to present two elementary, but useful, facts concerning actions on uniformly convex spaces. We demonstrate how each of them can be used in an alternative proof of the triviality of the first $L_p$-cohomology of…
This is a short expository account of the regularity lemma for stable graphs proved by the authors, with some comments on the model theoretic context, written for a general logical audience.
We consider several novel aspects of unique factorization in formal languages. We reprove the familiar fact that the set uf(L) of words having unique factorization into elements of L is regular if L is regular, and from this deduce an…
Akama et al. systematically studied an arithmetical hierarchy of the law of excluded middle and related principles in the context of first-order arithmetic. In that paper, they first provide a prenex normal form theorem as a justification…
In this paper, for a given finitely generated algebra (an algebraic structure with arbitrary operations and no predicates) A we study finitely generated limit algebras of A, approaching them via model theory and algebraic geometry. Along…
We checked that the distribution of words in text should uniform, which gives Heaps' law as natural result, that is, the number of types of words can be expressed as a power law of the number of tokens within text. We developed a…
When regularity lemmas were first developed in the 1970s, they were described as results that promise a partition of any graph into a ``small'' number of parts, such that the graph looks ``similar'' to a random graph on its edge subsets…
Zipf's law is just one out of many universal laws proposed to describe statistical regularities in language. Here we review and critically discuss how these laws can be statistically interpreted, fitted, and tested (falsified). The modern…
The general methods which are powerful for the necessity of bounded commutators are given. As applications, some necessary conditions for bounded commutators are first obtained in certain endpoint cases, and several new characterizations of…
We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic…
In this note I present the main ideas of my proposal about the theoretical framework that could underlie, and therefore "unify", Quantum Mechanics and Relativity, and I briefly summarize the implications and predictions.