Related papers: Finite canonization

Let E_n={x_i=1, x_i+x_j=x_k, x_i*x_j=x_k: i,j,k \in {1,...,n}}. We prove: (1) there is an algorithm that for every computable function f:N-->N returns a positive integer m(f), for which a second algorithm accepts on the input f and any…

Fine's influential Canonicity Theorem states that if a modal logic is determined by a first-order definable class of Kripke frames, then it is valid in its canonical frames. This article reviews the background and context of this result,…

For integers $k\ge 2$ and $N\ge 2k+1$ there are $k!2^k$ canonical orderings of the edges of the complete $k$-uniform hypergraph with vertex set $[N] = \{1,2,\dots, N\}$. These are exactly the orderings with the property that any two subsets…

Quantifier-elimination or model-completeness of the affine part of some classical first order theories are proved.

In this article, we prove two new versions of a theorem proven by Efron in [Efr65]. Efron's theorem says that if a function $\phi : \mathbb{R}^2 \rightarrow \mathbb{R}$ is non-decreasing in each argument then we have that the function $s…

We introduce and study some variants of a notion of canonical set theoretical truth. By this, we mean truth in a transitive proper class model $M$ of ZFC that is uniquely characterized by some $\in$-formula. We show that there are…

The process of canonical quantization is redefined so that the classical and quantum theories coexist when \hbar>0, just as they do in the real world. This analysis not only supports conventional procedures, it also reveals new quantization…

Many machine learning models leverage group invariance which is enjoyed with a wide-range of applications. For exploiting an invariance structure, one common approach is known as \emph{frame averaging}. One popular example of frame…

We present a theorem which generalizes the classical Euler's theorem on congruencies: if $(a,m)=1$ then $a^ \phi(m) \equiv 1 (mod m)$ for the case when $a$ and $m$ are not relatively primes.

We show that that a certain class of semi-proper iterations does not add omega-sequences. As a result, starting from suitable large cardinals one can obtain a model in which the Continuum Hypothesis holds and every function from omega_1 to…

A recent refinement of Ker\'ekj\'art\'o's Theorem has shown that in $\mathbb R$ and $\mathbb R^2$ all $\mathcal C^l$-solutions of the functional equation $f^n =\textrm{Id}$ are $\mathcal C^l$-linearizable, where $l\in \{0,1,\dots \infty\}$.…

We give a generalization of Kung's theorem on critical exponents of linear codes over a finite field, in terms of sums of extended weight polynomials of linear codes. For all i=k+1,...,n, we give an upper bound on the smallest integer m…

Let $C({\mathbb R}^n)$ denote the set of real valued continuous functions defined on ${\mathbb R}^n$. We prove that for every $n\ge 2$ there are positive numbers $\lambda _1 , \ldots , \lambda _n$ and continuous functions $\phi_1 ,\ldots ,…

This manuscript explores many convolution (restricted summation) type sequences via certain types of matrix based factorizations that can be used to express their generating functions. The last primary (non-appendix) section of the thesis…

We define an enumerative function F(n,k,P,m) which is a generalization of binomial coefficients. Special cases of this function are also power function, factorials, rising factorials and falling factorials. The first section of the paper is…

Let X,X_1,X_2,... be independent identically distributed random variables and let h(x,y)=h(y,x) be a measurable function of two variables. It is shown that the bounded law of the iterated logarithm, $\limsup_n (n\log\log n)^{-1}|\sum_{1<=…

We prove that for every equivalence relation on a barrier on the space $\langle FIN^{[\infty]}_k,\leq,r\rangle$, for any $k$, there exists $Y\in FIN_k^{[\infty]}$ so that the restriction of the coloring on $\langle Y\rangle$ is canonical.

In [5], Hjorth proved that for every countable ordinal $\alpha$, there exists a complete $\mathcal{L}_{\omega_1,\omega}$-sentence $\phi_\alpha$ that has models of all cardinalities less than or equal to $\aleph_\alpha$, but no models of…

Sets of solutions to finite systems of equations in a free group, are equivalent to sets of homomorphisms from a fixed f.p. group into a free group. The latter can be encoded in a diagram, the construction of which is valid also for f.g.…

The aim of this paper is to prove characterization theorems for field homomorphisms. More precisely, the main result investigates the following problem. Let $n\in \mathbb{N}$ be arbitrary, $\mathbb{K}$ a field and $f_{1}, \ldots,…