Related papers: A generic absoluteness principle consistent with l…

The primary purpose of this article is to show that a certain natural set of axioms yields a completeness result for continuous first-order logic. In particular, we show that in continuous first-order logic a set of formulae is (completely)…

We prove: $\mathbf{Theorem}$ Let $K$ be a universal class. If $K$ is categorical in cardinals of arbitrarily high cofinality, then $K$ is categorical on a tail of cardinals. The proof stems from ideas of Adi Jarden and Will Boney, and also…

Quantum repeaters promise to deliver long-distance entanglement overcoming noise and loss in realistic quantum channels. A promising class of repeaters, based on atomic ensemble quantum memories and linear optics, follow the proposal by…

We continue the development of the theory of infinitesimal Lipschitz equivalence, showing the genericity of the condition for families of hypersurfaces with isolated singularities.

We consider an abstract space of measurable linear cocycles and we assume the availability in this space of some appropriate uniform large deviation type estimates. Under these hypotheses we establish the continuity of the Oseledets…

It is shown that the resurrection axiom and the maximality principle may be consistently combined for various iterable forcing classes. The extent to which resurrection and maximality overlap is explored via the local maximality principle.

Compositional generalization is the capability of a model to understand novel compositions composed of seen concepts. There are multiple levels of novel compositions including phrase-phrase level, phrase-word level, and word-word level.…

These notes present a compact and self-contained approach to iterated forcing with a particular emphasis on semiproper forcing. We tried to make our presentation accessible to any scholar who has some familiarity with forcing and boolean…

Large Language Models (LLMs) are expected to be predictable and trustworthy to support reliable decision-making systems. Yet current LLMs often show inconsistencies in their judgments. In this work, we examine logical preference consistency…

Continual learning (CL) refers to a machine learning paradigm that learns continuously without forgetting previously acquired knowledge. Thereby, major difficulty in CL is catastrophic forgetting of preceding tasks, caused by shifts in data…

This paper proposes a new notion of typical sequences on a wide class of abstract alphabets (so-called standard Borel spaces), which is based on approximations of memoryless sources by empirical distributions uniformly over a class of…

We revisit the problem of general identifiability originally introduced in [Lee et al., 2019] for causal inference and note that it is necessary to add positivity assumption of observational distribution to the original definition of the…

We unveil that internal representations in large language models (LLMs) serve as reliable proxies of learned knowledge, and propose RECALL, a novel representation-aware model merging framework for continual learning without access to…

We prove that the strong polarized relation of $\theta$ above $\omega$ applied simultaneously for every cardinal in the interval $[\aleph_1,\aleph]$ is consistent. We conclude that this positive relation is consistent for every cardinal…

We devise an abstract, modular scheme to prove continuity of the Lyapunov exponents for a general class of linear cocycles. The main assumption is the availability of appropriate large deviation type (LDT) estimates which are uniform in the…

Shelah shows that certain revised countable support (RCS) iterations do not add reals. His motivation is to establish the independence (relative to large cardinals) of Avraham's problem on the existence of uncountable non-constuctible…

Using the consistency of some large cardinals we produce a model of Set Theory in which the generalized continuum hypothesis holds and for some torsion-free abelian group G of cardinality aleph_{omega +1} and for some torsion group T,…

We verify a confluence result for the rewriting calculus of the linear category introduced in our previous paper. Together with the termination result proved therein, the generalized coherence theorem for linear category is established.…

We formulate and prove (in {\sf ZFC}) a strong coloring theorem which holds at successors of singular cardinals, and use it to answer several questions concerning Shelah's principle $Pr_1(\mu^+,\mu^+,\mu^+,\cf(\mu))$ for singular $\mu$.

We construct generalized coherent states (GCS) of a massive accelerated particle. This example is an important step in studying coherent states (CS) for systems with an unbounded motion and a continuous spectrum. First, we represent quantum…