Zobrazeno 1 - 10
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pro vyhledávání: '"Quinn, Frank A."'
Autor:
Quinn, Frank
This article was motivated by the discovery of a potential new foundation for mainstream mathematics. The goals are to clarify the relationships between primitives, foundations, and deductive practice; to understand how to determine what is, or isn't
Externí odkaz:
http://arxiv.org/abs/2407.02507
Autor:
Quinn, Frank
In "Object generators, relaxed sets, and a foundation for mathematics", we introduced ``object generators'', a logical environment much more general than set theory. Inside this we found a `relaxed' version of set theory. That paper is focused on con
Externí odkaz:
http://arxiv.org/abs/2210.07280
Autor:
Quinn, Frank
Object generators are essentially the "object" primitives of category theory, and can usually be thought of as "collections of elements". We develop a logical context with these and their morphisms as primitives, and four straightforward axioms. The
Externí odkaz:
http://arxiv.org/abs/2110.01489
Autor:
Quinn, Frank
We begin with a context more general than set theory. The basic ingredients are essentially the object and functor primitives of category theory, and the logic is weak, requiring neither the Law of Excluded Middle nor quantification. Inside this we f
Externí odkaz:
http://arxiv.org/abs/2009.08867
Autor:
Quinn, Frank
This paper is one of a series in which elementary-education practice is analyzed by comparison with the history of mathematics, mathematical structure, modern practice, and (occasionally) cognitive neuroscience. The primary concerns are: Why do so ma
Externí odkaz:
http://arxiv.org/abs/1311.2235
Autor:
Quinn, Frank
A mostly expository account of old questions about the relationship between polyhedra and topological manifolds. Topics are old topological results, new gauge theory results (with speculations about next directions), and history of the questions.
Externí odkaz:
http://arxiv.org/abs/1310.7644
Publikováno v:
Journal of Topology, 4 (2011), 505-528
We use controlled topology applied to the action of the infinite dihedral group on a partially compactified plane and deduce two consequences for algebraic K-theory. The first is that the family in the K-theoretic Farrell-Jones conjecture can be redu
Externí odkaz:
http://arxiv.org/abs/1002.3702
Autor:
Quinn, Frank
The controlled end and h-cobrodism theorems (Ends of maps I, 1979) are used to give quick proofs of the Top/PL and PL/DIFF product structure theorems.
Comment: 6 pages
Comment: 6 pages
Externí odkaz:
http://arxiv.org/abs/math/0610131
Autor:
Quinn, Frank
Controlled $K$-theory is used to show that algebraic $K$-theory of virtually abelian groups is described by an assembly map defined using possibly-infinite hyperelementary subgroups. The Farrell-Jones summand (coming from infinite subgroups) is param
Externí odkaz:
http://arxiv.org/abs/math/0509294
Autor:
Quinn, Frank
Withdrawn May 2005. There is an error in the even-dimensional case of the proof in the April 2005 version. The hoped-for 4-dimensional applications are unlikely to survive the repairs.
Comment: April 2005 version withdrawn May 2005 due to an err
Comment: April 2005 version withdrawn May 2005 due to an err
Externí odkaz:
http://arxiv.org/abs/math/0504258