相关论文: The Goebbellian Syndrome
In a recent paper (Phys. Rev. A 105, 042220 (2022)), Daley et al claim that some superdeterministic models are disfavoured against standard quantum mechanics, because such models overfit the statistics of a Bell-type experiment which the…
If M is a nonstandard model of Peano Arithmetic, then M is lofty iff M has a simple elementary extension that is recursively saturated. This had previously been known for countable M.
The proliferation of probable prime tests in recent years has produced a plethora of definitions with the word ``pseudoprime'' in them. Examples include pseudoprimes, Euler pseudoprimes, strong pseudoprimes, Lucas pseudoprimes, strong Lucas…
It was established by Jensen in 1970 that there is a generic extension $L[a]$ of the constructible universe $L$ by a real $a\not\in L$ such that $a$ is $\varDelta^1_3$ in $L[a]$. Jensen's forcing construction has found a number of…
The new perspectives on ABC and Bayesian model criticisms presented in Ratmann et al.(2009) are challenging standard approaches to Bayesian model choice. We discuss here some issues arising from the authors' approach, including prior…
By affine arithmetic is meant the set of affine consequences of Peano arithmetic. This is a continuous theory which is studied in the framework of affine logic, a sublogic of continuous logic. Affine arithmetic is undecidable. Also, its…
The statement of E.R. Loubenets, Phys. Rev. A 69, 042102 (2004), that separable states can violate classical probabilistic constraints is based on a misleading definition of classicality, which is much narrower than Bell's concept of local…
The aim of this work is to show that contemporary mathematics, including Peano arithmetic, is inconsistent, to construct firm foundations for mathematics, and to begin building on these foundations.
A number of misleading or incorrect comments by C.Giunti on seven arXiv preprints that I have written on the theory of neutrino oscillations are discussed. The essential new features of my approach are also briefly reviewed
The present paper shows meta-programming turn programming, which is rich enough to express arbitrary arithmetic computations. We demonstrate a type system that implements Peano arithmetics, slightly generalized to negative numbers. Certain…
Nonlinear longitudinal proportional effect models have been proposed to improve power and provide direct estimates of the proportional treatment effect in randomized clinical trials. These models assume a fixed proportional treatment effect…
The predicate complementary to the well-known Godel's provability predicate is defined. From its recursiveness new consequences concerning the incompleteness argumentation are drawn and extended to new results of consistency, completeness…
To steer language models towards truthful outputs on tasks which are beyond human capability, previous work has suggested training models on easy tasks to steer them on harder ones (easy-to-hard generalization), or using unsupervised…
The belief that numbers offer a single, objective description of reality overlooks a crucial truth: data does not speak for itself. Every dataset results from choices-what to measure, how, when, and with whom-which inevitably reflect…
We observe several facts and make conjectures about commutative algebras satisfying the Jacobi identity. The central question is which of those algebras admit a faithful representation (i.e., in Lie parlance, satisfy the Ado theorem, or, in…
This paper presents a new representation of natural numbers and discusses its consequences for computability and computational complexity. The paper argues that the introduction of the first Peano axiom in the traditional definition of…
This article discusses a number of incorrect statements appearing in textbooks on data analysis, machine learning, or computational methods; the common theme in all these cases is the relevance and application of statistics to the study of…
A crucial input into causal inference is the imputed counterfactual outcome. Imputation error can arise because of sampling uncertainty from estimating the prediction model using the untreated observations, or from out-of-sample information…
This is a survey of results on definability and undefinability in models of arithmetic. The goal is to present a stark difference between undefinability results in the standard model and much stronger versions about expansions of…
We present a different combinatorial interpretations of Lucas and Gibonacci numbers. Using these interpretations we prove several new identities, and simplify the proofs of several known identities. Some open problems are discussed towards…