Related papers: Reflection Principles in ZFU
In this paper, we consider certain cardinals in ZF (set theory without AC, the Axiom of Choice). In ZFC (set theory with AC), given any cardinals C and D, either C <= D or D <= C. However, in ZF this is no longer so. For a given infinite…
This paper exposes a contradiction in the Zermelo-Fraenkel set theory with the axiom of choice (ZFC). While Godel's incompleteness theorems state that a consistent system cannot prove its consistency, they do not eliminate proofs using a…
In this article, we introduce a new general definition of fractional derivative and fractional integral, which depends on an unknown kernel. By using these definitions, we obtain the basic properties of fractional integral and fractional…
Partial Rejection Sampling is an algorithmic approach to obtaining a perfect sample from a specified distribution. The objects to be sampled are assumed to be represented by a number of random variables. In contrast to classical rejection…
The only relativistic reflection model that implements a parameter relating the intensity incident on an accretion disk to the observed intensity is relxill. The parameter used in earlier versions of this model, referred to as the…
Reward Models (RMs) are critical components in the Reinforcement Learning from Human Feedback (RLHF) pipeline, directly determining the alignment quality of Large Language Models (LLMs). Recently, Generative Reward Models (GRMs) have…
In this paper we study the joint distributions of the telegraph process and its maximum conditioned on the number of changes of direction and the initial velocity. We prove that in the case of positive starting velocity, a form of the…
We show that the Proper Forcing Axiom implies the Singular Cardinal Hypothesis. The proof is by interpolation and uses the Mapping Reflection Principle.
The purpose of this paper is to present some results which suggest that the Singular Cardinals Hypothesis follows from the Proper Forcing Axiom. What will be proved is that a form of simultaneous reflection follows from the Set Mapping…
We present a system of axioms motivated by a topological intuition: The set of subsets of any set is a topology on that set. On the one hand, this system is a common weakening of Zermelo-Fraenkel set theory ZF, the positive set theory GPK…
Many machine learning tasks admit multiple models that perform almost equally well, a phenomenon known as predictive multiplicity. A fundamental source of this multiplicity is observational multiplicity, which arises from the stochastic…
We demonstrate that theories $\text{Z}^-$, $\text{ZF}^-$, $\text{ZFC}^-$ (minus means the absence of the Power Set axiom) and $\text{PA}_2$, $\text{PA}_2^-$ (minus means the absence of the Countable Choice schema) are equiconsistent to each…
The work argues the principle of equivalence to be a theorem and not a principle (in a sense of an axiom). It contains a detailed analysis of the concepts of normal and inertial frame of reference. The equivalence principle is proved to be…
Self-reflection is important metacognitive skill, enabling students to build coherence into their learning and embed content in a broader context. While various pedagogical techniques exist to encourage student reflection, little research…
The notion of a "root base" together with its geometry plays a crucial role in the theory of finite and affine Lie theory. However, it is known that such a notion does not exist for the recent generalizations of finite and affine root…
In this note we study several topics related to the schema of local reflection $\mathsf{Rfn}(T)$ and its partial and relativized variants. Firstly, we introduce the principle of uniform reflection with $\Sigma_n$-definable parameters,…
Extending Aanderaa's classical result that $\pi^1_1<\sigma^1_1$, we determine the order between any two patterns of iterated $\Sigma^1_1$- and $\Pi^1_1$-reflection. We show that this \emph{linear reflection order} is a prewellordering of…
Let $X$ be a nonempty real variety that is invariant under the action of a reflection group $G$. We conjecture that if $X$ is defined in terms of the first $k$ basic invariants of $G$ (ordered by degree), then $X$ meets a $k$-dimensional…
Two bases of states are presented for modules of the graded parafermionic conformal field theory associated to the coset $\osp(1,2)_k/\uh(1)$. The first one is formulated in terms of the two fundamental (i.e., lowest dimensional)…
A set of general physical principles is proposed as the structural basis for the theory of complex systems. First the concept of harmony is analyzed and its different aspects are uncovered. Then the concept of reflection is defined and…