相关论文: Iterating the recursively Mahlo operations
In this note we axiomatize the $\Pi_{k+1}$-consequences in the set theory ${\sf KP}\Pi_{N}$ for $\Pi_{N}$-reflecting universes in terms of iterations of $\Pi_{i}$-recursively Mahlo operations for $1\leq k\leq i<N$.
The set theory KP$\Pi_{N+1}$ for $\Pi_{N+1}$-reflecting universes is shown to be $\Pi_{N+1}$-conservative over iterations of $\Pi_{N}$-recursively Mahlo operations for each $N\geq 2$.
We consider extensions of the language of Peano arithmetic by transfinitely iterated truth definitions satisfying uniform Tarskian biconditionals. Without further axioms, such theories are known to be conservative extensions of the original…
We give a method of solution to the problem of iterating holomorphic functions to fractional or complex heights. We construct an auxiliary function from natural iterates of a holomorphic function; the auxiliary function will be…
We introduce a simple lattice model in which percolation is constructed on top of critical percolation clusters, and show that it can be repeated recursively any number $n$ of generations. In two dimensions, we determine the percolation…
Recurrence networks are complex networks, constructed from time series data, having several practical applications. Though their properties when constructed with the threshold value \epsilon chosen at or just above the percolation threshold…
In this paper we study the problem of constructing non-trivial subtowers and supertowers of recursive towers of function fields over finite fields.
We study random independent and identically distributed iterations of functions from an iterated function system of homeomorphisms on the circle which is minimal. We show how such systems can be analyzed in terms of iterated function…
The repetition threshold is the smallest real number $\alpha$ such that there exists an infinite word over a $k$-letter alphabet that avoids repetition of exponent strictly greater than $\alpha$. This notion can be generalized to graph…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…
Recently, motion generation by machine learning has been actively researched to automate various tasks. Imitation learning is one such method that learns motions from data collected in advance. However, executing long-term tasks remains…
We derive, in order of magnitude, the observed astrophysical and cosmological scales in the Universe, from neutron stars to superclusters of galaxies, up to, asymptotically, the observed radius of the Universe. This result is obtained by…
Transformer models have established new benchmarks in natural language processing; however, their increasing depth results in substantial growth in parameter counts. While existing recurrent transformer methods address this issue by…
The problem of reconstructing a sequence of independent and identically distributed symbols from a set of equal size, consecutive, fragments, as well as a dependent reference sequence, is considered. First, in the regime in which the…
In this paper, we show that theory of processes can be reduced to the theory of spatial logic. Firstly, we propose a spatial logic SL for higher order pi-calculus, and give an inference system of SL. The soundness and incompleteness of SL…
Transformers are able to perform reasoning tasks, however the intrinsic mechanism remains widely open. In this paper we propose a set of information propagation rules based on Transformers and utilize symbolic reasoning tasks to…
We describe an iterable construction of THH for an E_n ring spectrum. The reduced version is an iterable bar construction and its n-th iterate gives a model for the shifted cotangent complex at the augmentation, representing reduced…
We conjecture that for a strongly minimal theory T in a finite signature satisfying the Zilber Trichotomy, there are only three possibilities for the recursive spectrum of T: all countable models of T are recursively presentable; none of…
The top of the attractor $A$ of a hyperbolic iterated function system $\left\{ f_{i}:\mathbb{R}^{n}\rightarrow\mathbb{R}^{n}|i=1,2,\dots,M\right\} $ is defined and used to extend self-similar tilings to overlapping systems. The theory…
We apply an iterative reconstruction method to galaxy mocks in redshift space obtained from $N$-body simulations. Comparing the two-point correlation functions for the reconstructed density field, we find that although the performance is…