Related papers: Canonical immunity and genericity
We present some results about generics for computable Mathias forcing. The $n$-generics and weak $n$-generics in this setting form a strict hierarchy as in the case of Cohen forcing. We analyze the complexity of the Mathias forcing…
Revisiting the thirty years-old notions of resource-bounded immunity and simplicity, we investigate the structural characteristics of various immunity notions: strong immunity, almost immunity, and hyperimmunity as well as their…
Monomial ideals which are generic with respect to either their generators or irreducible components have minimal free resolutions derived from simplicial complexes. For a generic monomial ideal, the associated primes satisfy a saturated…
This paper is a companion article to our previous paper (J. Stat. Phys. 119, 1283 (2005), cond-mat/0408681), which introduced a generalized canonical ensemble obtained by multiplying the usual Boltzmann weight factor $e^{-\beta H}$ of the…
There exist two notions of typicality in computability theory, namely, genericity and randomness. In this article, we introduce a new notion of genericity, called partition genericity, which is at the intersection of these two notions of…
In 2012, inspired by developments in group theory and complexity, Jockusch and Schupp introduced generic computability, capturing the idea that an algorithm might work correctly except for a vanishing fraction of cases. However, we observe…
A Ramsey-like theorem is a statement of the form ``For every 2-coloring of $[\mathbb{N}]^2$, there exists an infinite set~$H \subseteq \mathbb{N}$ such that $[H]^2$ avoids some pattern''. We prove that none of these statements are…
We give solutions to two of the questions in a paper by Brendle, Brooke-Taylor, Ng and Nies. Our examples derive from a 2014 construction by Khan and Miller as well as new direct constructions using martingales. At the same time, we…
Currently there are two main approaches to describe how quantum statistical physics emerges from an isolated quantum many-body system in a pure state: Canonical Typicality (CT) and Eigenstate Thermalization Hypothesis (ETH). These two…
In this short note, we introduce a generalization of the canonical base property, called transfer of internality on quotients. A structural study of groups definable in theories with this property yields as a consequence infinitely many new…
We compare two different notions of generic expansions of countable saturated structures. One kind of genericity is related to model-companions and to amalgamation constructions \'a la Hrushovski-Fra\"iss\'e. Another notion of generic…
A new notion of typicality for arbitrary probability measures on standard Borel spaces is proposed, which encompasses the classical notions of weak and strong typicality as special cases. Useful lemmas about strong typical sets, including…
In this survey paper we first present the main properties of sequentially Cohen-Macaulay modules. Some basic examples are provided to help the reader with quickly getting acquainted with this topic. We then discuss two generalizations of…
Starting from the $\rm{GCH},$ we build a cardinal and $\rm{GCH}$ preserving generic extension of the universe, in which there exists a set $A \subseteq \omega_2$ of size $\aleph_2$ so that every countably infinite subset of $A$ or $\omega_2…
In this paper, the notion of generic transversality and its characterization are given. The characterization is also a further improvement of the basic transversality result and its strengthening which was given by John Mather.
Conventional canonical quantization procedures directly link various c-number and q-number quantities. Here, we advocate a different association of classical and quantum quantities that renders classical theory a natural subset of quantum…
With the control of ever more complex quantum systems becoming a reality, new scenarios are emerging where generalizations of the most foundational aspects of statistical quantum mechanics are imperative. In such experimental scenarios the…
We discuss invariants of Cohen-Macaulay local rings that admit a canonical module $\omega$. Attached to each such ring R, when $\omega$ is an ideal, there are integers--the type of R, the reduction number of $\omega$--that provide valuable…
The Cohen-Lenstra heuristic is a universal principle that assigns to each group a probability that tells how often this group should occur "in nature". The most important, but not the only, applications are sequences of class groups, which…
The Bayesian framework is a well-studied and successful framework for inductive reasoning, which includes hypothesis testing and confirmation, parameter estimation, sequence prediction, classification, and regression. But standard…