A geometric proof of the mumford compactness theorem

1988 ◽  
pp. 174-181
Author(s):  
Friedrich Tomi ◽  
A. J. Tromba
Keyword(s):  
Compactness Theorem ◽  
Geometric Proof

scholarly journals Interpretability over peano arithmetic

1999 ◽  
Vol 64 (4) ◽  
pp. 1407-1425
Author(s):  
Claes Strannegård
Keyword(s):  
Modal Logic ◽  
Completeness Theorem ◽  
Peano Arithmetic ◽  
Embedding Theorem ◽  
Compactness Theorem ◽  
Partial Answer ◽  
Recursively Enumerable ◽  
Recursively Enumerable Sets ◽  
Interpretability Logic

AbstractWe investigate the modal logic of interpretability over Peano arithmetic. Our main result is a compactness theorem that extends the arithmetical completeness theorem for the interpretability logic ILMω. This extension concerns recursively enumerable sets of formulas of interpretability logic (rather than single formulas). As corollaries we obtain a uniform arithmetical completeness theorem for the interpretability logic ILM and a partial answer to a question of Orey from 1961. After some simplifications, we also obtain Shavrukov's embedding theorem for Magari algebras (a.k.a. diagonalizable algebras).

A Geometric Proof of lim d →0 +(-dln d) = 0

1992 ◽  
Vol 23 (3) ◽  
pp. 209
Author(s):  
John H. Mathews
Keyword(s):  
Geometric Proof

A Lattice-Geometric Proof of Wedderburn’s Theorem

1993 ◽  
Vol 23 (3-4) ◽  
pp. 384-386 ◽  
Author(s):  
Stefan E. Schmidt
Keyword(s):  
Geometric Proof

A Simple Geometric Proof of the Addition Formula for the Sine

1994 ◽  
Vol 25 (3) ◽  
pp. 229
Author(s):  
Jeffrey Li-chieh Ho
Keyword(s):  
Geometric Proof ◽  
Addition Formula

A Geometric Proof of Machin's Formula

1990 ◽  
Vol 63 (5) ◽  
pp. 336
Author(s):  
Roger B. Nelsen
Keyword(s):  
Geometric Proof

scholarly journals Non-defectivity of Grassmannian bundles over a curve

2016 ◽  
Vol 27 (07) ◽  
pp. 1640002 ◽  
Author(s):  
Insong Choe ◽  
George H. Hitching
Keyword(s):  
Vector Bundles ◽  
Manuscripta Math ◽  
Maximal Degree ◽  
Geometric Proof ◽  
Secant Varieties ◽  
Grassmann Bundle ◽  
Positive Rank

Let [Formula: see text] be the Grassmann bundle of two-planes associated to a general bundle [Formula: see text] over a curve [Formula: see text]. We prove that an embedding of [Formula: see text] by a certain twist of the relative Plücker map is not secant defective. This yields a new and more geometric proof of the Hirschowitz-type bound on the isotropic Segre invariant for maximal isotropic sub-bundles of orthogonal bundles over [Formula: see text], analogous to those given for vector bundles and symplectic bundles in [I. Choe and G. H. Hitching, Secant varieties and Hirschowitz bound on vector bundles over a curve, Manuscripta Math. 133 (2010) 465–477, I. Choe and G. H. Hitching, Lagrangian sub-bundles of symplectic vector bundles over a curve, Math. Proc. Cambridge Phil. Soc. 153 (2012) 193–214]. From the non-defectivity, we also deduce an interesting feature of a general orthogonal bundle of even rank over [Formula: see text], contrasting with the classical and symplectic cases: a general maximal isotropic sub-bundle of maximal degree intersects at least one other such sub-bundle in positive rank.

scholarly journals Myers-type compactness theorem with the Bakry-Emery Ricci tensor

2021 ◽  
Vol 73 (3) ◽  
Author(s):  
Seungsu Hwang ◽  
Sanghun Lee
Keyword(s):  
Ricci Tensor ◽  
Compactness Theorem
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