Inconsistent Countable Set in Second Order ZFC and Nonexistence of the Strongly Inaccessible Cardinals

British Journal of Mathematics and Computer Science 9 (5):380-393 (2015)
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Abstract

In this article we derived an important example of the inconsistent countable set in second order ZFC (ZFC_2) with the full second-order semantics. Main results: (i) :~Con(ZFC2_); (ii) let k be an inaccessible cardinal, V is an standard model of ZFC (ZFC_2) and H_k is a set of all sets having hereditary size less then k; then : ~Con(ZFC + E(V)(V = Hk)):

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Citations of this work

There is No Standard Model of ZFC and ZFC_2. Part I.Jaykov Foukzon - 2017 - Journal of Advances in Mathematics and Computer Science 2 (26):1-20.
The Solution of the Invariant Subspace Problem. Complex Hilbert space. Part I.Jaykov Foukzon - 2022 - Journal of Advances in Mathematics and Computer Science 37 (10):51-89.

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References found in this work

Completeness in the theory of types.Leon Henkin - 1950 - Journal of Symbolic Logic 15 (2):81-91.
Toward a Theory of Second-Order Consequence.Augustín Rayo & Gabriel Uzquiano - 1999 - Notre Dame Journal of Formal Logic 40 (3):315-325.
First-order logic, second-order logic, and completeness.Marcus Rossberg - 2004 - In Vincent F. Hendricks (ed.), First-order logic revisited. Berlin: Logos. pp. 303-321.
Warning signs of a possible collapse of contemporary mathematics.Edward Nelson - 2011 - In Michał Heller & W. H. Woodin (eds.), Infinity: new research frontiers. New York: Cambridge University Press. pp. 76.

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