scholarly journals Nonstandard topological extensions

1975 ◽  
Vol 13 (2) ◽  
pp. 269-290 ◽  
Author(s):  
Robert A. Herrmann
Keyword(s):  
General Study ◽  
Ultrafilter Extensions

This paper investigates the nonstandard theory of filters on a non-empty meet-semi-lattice of sets and applies this theory to the general study of topological extensions Y for a space X. In particular, we apply this theory to Baire and quasi-H-closed extensions as well as Wallman type compactifications. Whereas these extensions have previously teen obtained and studied as types of ultrafilter extensions, we study them as subsets of an enlargement of X. Since X ⊂ Y ⊂ ◯ and the elements of X and Y - X are of the same set-theoretic type, these extensions appear more natural from the nonstandard viewpoint.

scholarly journals GRADED TWISTED CALABI–YAU ALGEBRAS ARE GENERALIZED ARTIN–SCHELTER REGULAR

2021 ◽  
pp. 1-54
Author(s):  
MANUEL L. REYES ◽  
DANIEL ROGALSKI
Keyword(s):  
Regularity Property ◽  
Graded Algebra ◽  
General Study ◽  
Locally Finite ◽  
Tensor Algebras ◽  
Finite Dimensional ◽  
Dimension 2 ◽  
Separable Algebras ◽  
Gk Dimension

Abstract This is a general study of twisted Calabi–Yau algebras that are $\mathbb {N}$ -graded and locally finite-dimensional, with the following major results. We prove that a locally finite graded algebra is twisted Calabi–Yau if and only if it is separable modulo its graded radical and satisfies one of several suitable generalizations of the Artin–Schelter regularity property, adapted from the work of Martinez-Villa as well as Minamoto and Mori. We characterize twisted Calabi–Yau algebras of dimension 0 as separable k-algebras, and we similarly characterize graded twisted Calabi–Yau algebras of dimension 1 as tensor algebras of certain invertible bimodules over separable algebras. Finally, we prove that a graded twisted Calabi–Yau algebra of dimension 2 is noetherian if and only if it has finite GK dimension.

scholarly journals MODEL STRUCTURES ON TRIANGULATED CATEGORIES

2014 ◽  
Vol 57 (2) ◽  
pp. 263-284 ◽  
Author(s):  
XIAOYAN YANG
Keyword(s):  
Proper Class ◽  
Triangulated Category ◽  
Triangulated Categories ◽  
General Study ◽  
Proper Class Of Triangles ◽  
Cotorsion Pairs ◽  
One To One ◽  
The Relationship ◽  
Model Structures

AbstractWe define model structures on a triangulated category with respect to some proper classes of triangles and give a general study of triangulated model structures. We look at the relationship between these model structures and cotorsion pairs with respect to a proper class of triangles on the triangulated category. In particular, we get Hovey's one-to-one correspondence between triangulated model structures and complete cotorsion pairs with respect to a proper class of triangles. Some applications are given.

Virtue Epistemology as Anti-luck Epistemology

2021 ◽  
Vol 58 (4) ◽  
pp. 77-94
Author(s):  
Alexey Z. Chernyak ◽  
Keyword(s):  
Critical Analysis ◽  
Virtue Epistemology ◽  
Propositional Knowledge ◽  
General Study ◽  
Intellectual Virtues ◽  
Mental Attitude ◽  
Justified Belief ◽  
The Status ◽  
Veritic Luck ◽  
Contemporary Epistemology

The idea that knowledge as an individual mental attitude with certain propositional content is not only true justified belief but a belief the truth of which does not result from any kind of luck, is widely spread in contemporary epistemology. This account is known as anti-luck epistemology. A very popular explanation of the inconsistency of that concept of knowledge with the luck-dependent nature of truth (so called veritic luck taking place when a subject’s belief could not be true if not by mere coincidence) presumes that the status of propositional knowledge crucially depends on the qualities of actions that result in the corresponding belief, or processes backing them, which reflect the socalled intellectual virtues mainly responsible for subject’s relevant competences. This account known as Virtue Epistemology presumes that if a belief is true exclusively or mainly due to its dependence on intellectual virtues, it just cannot be true by luck, hence no place for lucky knowledge. But this thesis is hard to prove given the existence of true virtuous beliefs which could nevertheless be false if not for some lucky (for the knower) accident. This led to an appearance of virtue epistemological theories aimed specifically at an assimilation of such cases. Their authors try to represent the relevant situations as such where the contribution of luck is not crucial whereas the contribution of virtues is crucial. This article provides a critical analysis of the corresponding arguments as part of a more general study of the ability of Virtue Epistemology to provide justification for the thesis of incompatibility of propositional knowledge with veritic luck. It is shown that there are good reasons to doubt that Virtue Epistemology can do this.

scholarly journals Tautological rings of spaces of pointed genus two curves of compact type

2016 ◽  
Vol 152 (7) ◽  
pp. 1398-1420 ◽  
Author(s):  
Dan Petersen
Keyword(s):  
Hodge Structure ◽  
Galois Representation ◽  
Mixed Hodge Structure ◽  
Poincaré Duality ◽  
General Study ◽  
Compact Type ◽  
Poincare Duality ◽  
Tautological Ring ◽  
Genus Two ◽  
Tautological Rings

We prove that the tautological ring of ${\mathcal{M}}_{2,n}^{\mathsf{ct}}$, the moduli space of $n$-pointed genus two curves of compact type, does not have Poincaré duality for any $n\geqslant 8$. This result is obtained via a more general study of the cohomology groups of ${\mathcal{M}}_{2,n}^{\mathsf{ct}}$. We explain how the cohomology can be decomposed into pieces corresponding to different local systems and how the tautological cohomology can be identified within this decomposition. Our results allow the computation of $H^{k}({\mathcal{M}}_{2,n}^{\mathsf{ct}})$ for any $k$ and $n$ considered both as $\mathbb{S}_{n}$-representation and as mixed Hodge structure/$\ell$-adic Galois representation considered up to semi-simplification. A consequence of our results is also that all even cohomology of $\overline{{\mathcal{M}}}_{2,n}$ is tautological for $n<20$, and that the tautological ring of $\overline{{\mathcal{M}}}_{2,n}$ fails to have Poincaré duality for all $n\geqslant 20$. This improves and simplifies results of the author and Orsola Tommasi.

Off the Record: Unrecorded Legislative Votes, Selection Bias and Roll-Call Vote Analysis

2006 ◽  
Vol 36 (4) ◽  
pp. 691-704 ◽  
Author(s):  
CLIFFORD J. CARRUBBA ◽  
MATTHEW GABEL ◽  
LACEY MURRAH ◽  
RYAN CLOUGH ◽  
ELIZABETH MONTGOMERY ◽  
...  
Keyword(s):  
Random Sample ◽  
Selection Bias ◽  
European Parliament ◽  
Roll Call ◽  
General Study ◽  
Roll Call Vote ◽  
Legislative Voting ◽  
Sampling Problem ◽  
The Universe

Scholars often use roll-call votes to study legislative behaviour. However, many legislatures only conclude a minority of decisions by roll call. Thus, if these votes are not a random sample of the universe of votes cast, scholars may be drawing misleading inferences. In fact, theories over why roll-call votes are requested would predict selection bias based on exactly the characteristics of legislative voting that scholars have most heavily studied. This article demonstrates the character and severity of this sampling problem empirically by examining European Parliament vote data for a whole year. Given that many legislatures decided only a fraction of their legislation by roll call, these findings have potentially important implications for the general study of legislative behaviour.

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