We present a new approach to the invariant subspace problem for complex Hilbert spaces.This approach based on nonconservative Extension of the Model Theoretical NSA. Our main result will be that: if T is a bounded linear operator on an infinite-dimensional complex separable Hilbe...
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Research Article10.9734/jamcs/2022/v37i111721
The incompleteness of set theory ZFC leads one to look for natural extensions of ZFC in which one can prove statements wich appear as independent of ZFC but which look to be \true". In this paper we deal with set theory NC\(^{\#}{_\infty}_{\#}\) based on hyper infinitary logic wi...
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Research Article10.9734/jamcs/2022/v37i101717
The incompleteness of set theory \(Z F C\) leads one to look for natural nonconservative extensions of \(Z F C\) in which one can prove statements independent of \(Z F C\) which appear to be "true". One approach has been to add large cardinal axioms.Or, one can investigate second...
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Research Article10.9734/jamcs/2022/v37i730463
In this paper intuitionistic set theory INC#∞# in infinitary set theoretical language is considered. External induction principle in nonstandard intuitionistic arithmetic were derived. Non trivial application in number theory is considered.The Goldbach-Euler theorem is obtained w...
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Research Article10.9734/jamcs/2021/v36i830394
In this paper intuitionistic set theory INC# ∞# in infinitary set theoretical language is considered. External induction principle in nonstandard intuitionistic arithmetic were derived. Non trivial application in number theory is considered.The Goldbach-Euler theorem is obtained...
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Research Article10.9734/jamcs/2021/v36i430359
In this paper we view the rst order set theory ZFC under the canonical rst order semantics and the second order set theory ZFC2 under the Henkin semantics. Main results are: (i) Let MZFCst be a standard model of ZFC, then ¬Con(ZFC +∃MZFCst ). (ii) Let MZFC2st be a standard model...
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Research Article10.9734/JAMCS/2018/38773
This paper dealing with extension of the Einstein field equations using apparatus of contemporary generalization of the classical Lorentzian geometry named in literature Colombeau distributional geometry, see for example [1], [2], [3], [4], [5], [6], [7] and [32]. The regularizat...
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Research Article10.9734/BJMCS/2016/19235
In this paper we leave the neighborhood of the singularity at the origin and turn to the singularity at the horizon. Using nonlinear distributional geometry and Colombeau generalized functions it seems possible to show that the horizon singularity is not only a coordinate singula...
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Research Article10.9734/BJMCS/2015/16961
In this article we derived an important example of the inconsistent countable set in second order ZFC (ZFC2) with the full second-order semantics. Main results: (i) ¬Con(ZFC2), (ii) let k be an inaccessible cardinal and Hk is a set of all sets having hereditary size less then k,...
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Research Article10.9734/BJMCS/2015/16849