von Neumann universe: A perspective

Singh, D.; Singh, J.

doi:10.12988/ijcms.2007.07043

Cited by 4 publications

(4 citation statements)

References 3 publications

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“…It is observed in Drake and Singh [16], P. 190; that the axiom of universe is very close to the full second order version of cumulative type structure and, in turn, to Fraenkel's strong axiom of infinity (Levy [17]; Singh and Singh [18]). In Kruse [19], it is pointed out that the notions of Grothendieck universes and small super complete near model are equivalent.…”

Section: A Characterization Of the Universe For Categories And Multismentioning

confidence: 99%

Does the category of multisets require a larger universe than that of the category of sets?

Singh¹,

Isah²,

Alkali³

2013

pms

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In section 1, the concept of a category is briefly described. In section 2, it is elaborated how the concept of category is naturally intertwined with the existence of a universe of discourse much larger than what is otherwise sufficient for a large part of mathematics. It is also remarked that the extended universe for the category of sets is adequate for the category of multisets as well. In section 3, fundamentals required for adequately describing a category are extended to defining a multiset category, and some of its distinctive features are outlined. Mathematics Subject Classification: 18A05, 18A20, 18B99 134Dasharath Singh et al.

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Section: A Characterization Of the Universe For Categories And Multismentioning

confidence: 99%

Does the category of multisets require a larger universe than that of the category of sets?

Singh¹,

Isah²,

Alkali³

2013

pms

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“…These sets contain each natural number y (as defined in (1)). In this way we obtain (6). Then we see a blue bracket including all natural numbers (and all sets).…”

Section: ? } ?mentioning

confidence: 99%

“…We consider the axiom of infinity [4] [5] [8] , then the existence of N and Peano axioms [3]. Sets are considered with the usual graphical-symbolic notation {0, 1, 2, ...n} (see also [6] [7]). We starting with the sets-list {x|x ≤ y} ∀y ∈ N with all y taken together.…”

Section: Introductionmentioning

confidence: 99%

Inconsistency of ℕ with the set union operation

Cadeddu

2024

Preprint

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“…Also structure extended in to by L. S. Das, R. Nivas and V. N. Pathak [5]. In 1989, V. C. Gupta [6] studied on more generalized form structure satisfying where is a positive integer In addition, manifolds with structure satisfying fixed integer fixed odd integer have been defined and studied by A. Singh [7] and the complete and horizontal lifts of structure extended in to tangent bundle by A. Singh, R. K. Pandey and S. Khare [8]. In later times, M.D.…”

Section: Introductionmentioning

confidence: 99%

The General F_(a,λ) (K,T)- Structure Satisfying aF^K+λ^r F^T=0 on M^n and Lifts Problems Associated with the Structure

Çayir

2021

J. Sci. Arts

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In this paper our aim is to get the general structure equation which covers previously acquired structures. In this context this paper consists of three main sections. In the first section, we define the general F_(a,λ) (K,T)-structure satisfying aF^K+λ^r F^T=0,(F≠0,K≥3,T≥1 and (K≥T),a and λ are non zero complex numbers, r some finite integer) on manifold M^n and studied to give some special examples. The second part, we find the integrability conditions by calculating Nijenhuis tensors of the horizontal lifts of the general F_(a,λ) (K,T)-structure satisfying aF^K+λ^r F^T=0. Later, we get the results of Tachibana operators applied to vector and covector fields according to the horizontal lifts of the general F_(a,λ) (K,T)-structure in cotangent bundle T^* (M^n). In addition, we have studied to show the purity conditions of Sasakian metric with respect to the horizontal lifts of the structure. In the final section, all results obtained in the second section were investigated according to the complete and horizontal lifts of the general F_(a,λ) (K,T)-structure on tangent bundle T(M^n).

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von Neumann universe: A perspective

Abstract: In this commemorating note we attempt to show that the von Neumann universe V has a profound mathematical structure.

Cited by 4 publications

References 3 publications

Does the category of multisets require a larger universe than that of the category of sets?

Does the category of multisets require a larger universe than that of the category of sets?

Inconsistency of ℕ with the set union operation

The General F_(a,λ) (K,T)- Structure Satisfying aF^K+λ^r F^T=0 on M^n and Lifts Problems Associated with the Structure

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