Mathias, A.R.D. - Search Results - UAB Digital Repository of Documents

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Research literature, 2 records found

Research literature	2 records found

76 p, 446.3 KB

Weak systems of Gandy, Jensen and Devlin / Mathias, A. R. D. ; Centre de Recerca Matemàtica
In Part I, we formulate and examine some systems that have arisen in the study of the constructible hierarchy; we find numerous transitive models for them, among which are supertransitive models containing all ordinals that show that Devlin's system BS lies strictly between Gandy's systems PZ and BST'; and we use our models to show that BS fails to handle even the simplest rudimentary functions, and is thus inadequate for the use intended for it in Devlin's treatise. [...]
Centre de Recerca Matemàtica 2005 (Prepublicacions del Centre de Recerca Matemàtica ; 614)

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18 p, 233.1 KB

Epireflections and supercompact cardinals / Bagaria, Joan ; Casacuberta, Carles ; Mathias, A. R. D. ; Centre de Recerca Matemàtica
We prove that, under suitable assumptions on a category C, the existence of supercompact cardinals implies that every absolute epireflective class of objects of C is a small-orthogonality class. More precisely, if L is a localization functor on an accessible category C such that the unit morphism X→LX is an extremal epimorphism for all X, and the class of L-local objects is defined by an absolute formula with parameters, then the existence of a supercompact cardinal above the cardinalities of the parameters implies that L is a localization with respect to some set of morphisms.
Centre de Recerca Matemàtica 2007 (Prepublicacions del Centre de Recerca Matemàtica ; 740)

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2	Mathias, A. R. D.

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