منابع مشابه
Relative set theory: Strong stability
GRIST is an axiomatic framework for nonstandard set theory with many “levels of standardness.” The paper establishes a number of general consequences of GRIST, in particular, a very strong form of Transfer principle. 2010 Mathematics Subject Classification 26E35 (primary); 03E70, 03H05 (secondary)
متن کاملRelative set theory: Internal view
A nonstandard set theory with many levels of standardness was first proposed by Yves Péraire [28]. The theory GRIST formulated here is an extension of Péraire’s RIST. We prove that it is conservative and categorical over ZFC, and universal among theories of its kind. Technically, the paper carries out detailed analysis of the construction of internally iterated ultrapowers introduced in the aut...
متن کاملRelative set theory: Some external issues
The paper establishes equivalence of two axiomatizations of the relative set theory GRIST, examines dependence of nonstandard concepts on the choice of the level, and proves that several nonstandard definitions of Lebesgue measure are equivalent. The last section extends GRIST to a theory of external sets. 2000 Mathematics Subject Classification 26E35 (primary); 03E70, 03H05, 28E05 (secondary)
متن کاملStability Theory for Set Differential Equations
The formulation of set differential equations has an intrinsic disadvantage that the diameter of the solution is nondecreasing as time increases and therefore the behavior of solutions, in some cases, do not match with the solutions of ordinary differential equations from which set differential equations can be generated. In this paper an approach is provided to remove the disadvantage.
متن کاملUNCERTAINTY ANALYSIS OF STABILITY OF GRAVITY DAMS USING THE FUZZY SET THEORY
This paper introduces a methodology for considering the uncertainties in stability analysis of gravity dams. For this purpose, a conceptual model based on the fuzzy set theory and Genetic Algorithm (GA) optimization is developed to be coupled to a gravity dam analysis model. The uncertainties are represented by the fuzzy numbers and the GA is used to estimate in what...
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ژورنال
عنوان ژورنال: Journal of Logic and Analysis
سال: 2012
ISSN: 1759-9008
DOI: 10.4115/jla.2012.4.11