This article demonstrates the invalidity of Theorem VI in Gödel’s 1931, showing that propositions (15) and (16), derived from the definition 8.1, in its proof, are false in PA. Introduction. Developed as a consequence of the crisis of the foundation of mathematics due to the discovery of the antinomies, Hilbert’s formalism planned as criterions of adequacy for the axiomatic systems, the achieve...

s from the speci…c decision problem and aggregation rule in question. My exposition of this model follows the formalism introduced in List and Pettit (2002) and extended beyond standard propositional logic by Dietrich (2007a). There is a …nite set of (two or more) individuals, who have to make judgments on some propositions.3 Propositions are represented by sentences from propositional logic or...

We study a pair of Calabi–Yau threefolds X and M, fibered in non-principally polarized Abelian surfaces their duals, an equivalence $$D^b(X) \cong D^b(M)$$ , building on work Gross, Popescu, Bak, Schnell. Over the complex numbers, is simply connected while $$\pi _1(M) = (\mathbf {Z}/3)^2$$ . In characteristic 3, we find that M have different Hodge which would be impossible 0. appendix, give str...

the misconception (shubha) of absolute nonexistent – which we have named as paradox – is not an amusing brainteaser; rather, it is one the significant epistemological issues. its importance can be looked upon from two different viewpoints: research and educational. it is significant from the research viewpoint because it challenges propositions which constitute the foundation of our thinking an...

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