Models for smooth infinitesimal analysis
نویسندگان
چکیده
منابع مشابه
Comparing the Smooth and Dedekind Reals in Smooth Infinitesimal Analysis
Smooth infinitesimal analysis, SIA, is a theory formulated within higher-order intuitionistic logic and based on (at least) the following axioms: Axioms for the continuum, or smooth real line R. These include the usual axioms for a commutative ring with unit expressed in terms of two operations + and i , and two distinguished elements 0 ≠ 1. In addition we stipulate that R is a local ring, i.e....
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A remarkable development in twentieth-century mathematics is smooth infinitesimal analysis ("SIA"), introducing nilsquare and nilpotent infinitesimals, recovering the bulk of scientifically applicable classical analysis ("CA") without resort to the method of limits. Formally, however, unlike Robinsonian "nonstandard analysis", SIA conflicts with CA, deriving, e.g., "not every quantity is either...
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In this work a new approach to multidimensional geometry based on smooth infinitesimal analysis (SIA) is proposed. An embedded surface in this multidimensional geometry will look different for the external and internal observers: from the outside it will look like a composition of infinitesimal segments, while from the inside like a set of points equipped by a metric. The geometry is elastic. E...
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The goal of this paper is to give a method to compute the space of infinitesimal deformations of a double cover of a smooth algebraic variety. This research was inspired by the analysis of Calabi–Yau manifolds that arise as smooth models of double covers of P branched along singular octic surfaces ([4, 3]). It is of considerable interest to determine the Hodge numbers for these manifolds, but t...
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In this paper we study infinitesimal CR automorphisms of Levi degenerate hypersurfaces. We illustrate the recent general results of [18], [17], [15], on a class of concrete examples, polynomial models in C3 of the form Im w = Re (P (z)Q(z)), where P and Q are weighted homogeneous holomorphic polynomials in z = (z1, z2). We classify such models according to their Lie algebra of infinitesimal CR ...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1991
ISSN: 0001-8708
DOI: 10.1016/0001-8708(91)90022-y