Two notes on the Paris independence result

1981 ◽  
pp. 21-24
Author(s):  
Peter Aczel
Keyword(s):  
Independence Result

scholarly journals Independence of algebraic monodromy groups in compatible systems

2021 ◽  
Vol 27 (4) ◽  
Author(s):  
Federico Amadio Guidi
Keyword(s):  
Galois Representations ◽  
Global Function ◽  
Irreducible Decomposition ◽  
Global Function Fields ◽  
Normal Varieties ◽  
Independence Result ◽  
Monodromy Groups ◽  
Independence Results ◽  
Lisse Sheaves ◽  
General Method

AbstractIn this paper we develop a general method to prove independence of algebraic monodromy groups in compatible systems of representations, and we apply it to deduce independence results for compatible systems both in automorphic and in positive characteristic settings. In the abstract case, we prove an independence result for compatible systems of Lie-irreducible representations, from which we deduce an independence result for compatible systems admitting what we call a Lie-irreducible decomposition. In the case of geometric compatible systems of Galois representations arising from certain classes of automorphic forms, we prove the existence of a Lie-irreducible decomposition. From this we deduce an independence result. We conclude with the case of compatible systems of Galois representations over global function fields, for which we prove the existence of a Lie-irreducible decomposition, and we deduce an independence result. From this we also deduce an independence result for compatible systems of lisse sheaves on normal varieties over finite fields.

scholarly journals An Independence Result on Cotorsion Theories over Valuation Domains

2001 ◽  
Vol 243 (1) ◽  
pp. 294-320 ◽  
Author(s):  
S Bazzoni ◽  
L Salce
Keyword(s):  
Independence Result ◽  
Valuation Domains

scholarly journals On an independence result in the theory of lawless sequences

1983 ◽  
Vol 86 (2) ◽  
pp. 185-191
Author(s):  
Gerrit van der Hoeven ◽  
leke Moerdijk
Keyword(s):  
Independence Result

scholarly journals Countable Fréchet Boolean groups: An independence result

2009 ◽  
Vol 74 (3) ◽  
pp. 1061-1068 ◽  
Author(s):  
Jörg Brendle ◽  
Michael Hrušák
Keyword(s):  
Partial Answer ◽  
Independence Result

AbstractIt is relatively consistent with ZFC that every countable FUfin space of weight ℵ1 is metrizable. This provides a partial answer to a question of G. Gruenhage and P. Szeptycki [GS1].

An Independence Result Concerning Russell-Cardinals

2008 ◽  
Vol 31 (2) ◽  
pp. 173-177 ◽  
Author(s):  
Eleftherios Tachtsis
Keyword(s):  
Independence Result

Trees with random conductivities and the (reciprocal) inverse Gaussian distribution

1998 ◽  
Vol 30 (02) ◽  
pp. 409-424 ◽  
Author(s):  
O. E. Barndorff-Nielsen ◽  
A. E. Koudou
Keyword(s):  
Gaussian Distribution ◽  
Rooted Tree ◽  
Inverse Gaussian Distribution ◽  
Brownian Diffusion ◽  
Inverse Gaussian ◽  
Total Resistance ◽  
Conditional Model ◽  
Infinite Trees ◽  
Independence Result

Equipping the edges of a finite rooted tree with independent resistances that are inverse Gaussian for interior edges and reciprocal inverse Gaussian for terminal edges makes it possible, for suitable constellations of the parameters, to show that the total resistance is reciprocal inverse Gaussian (Barndorff-Nielsen 1994). This result is extended to infinite trees. Also, a connection to Brownian diffusion is established and, for the case of finite trees, an exact distributional and independence result is derived for the conditional model given the total resistance.

An Independence Result for Pinning for Ordinals

1979 ◽  
Vol s2-19 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Jean A. Larson
Keyword(s):  
Independence Result

Fred Appenzeller. An independence result in quadratic form theory: infinitary combinatorics applied to ε-Hermitian spaces. The journal of symbolic logic, vol. 54 (1989), pp. 689–699. - Otmar Spinas. Linear topologies on sesquilinear spaces of uncountable dimension. Fundamenta mathematicae, vol. 139 (1991), pp. 119–132. - James E. Baumgartner, Matthew Foreman, and Otmar Spinas. The spectrum of the Γ-invariant of a bilinear space. Journal of algebra, vol. 189 (1997), pp. 406–418. - James E. Baumgartner and Otmar Spinas. Independence and consistency proofs in quadratic form theory. The journal of symbolic logic, vol. 56 (1991), pp. 1195–1211. - Otmar Spinas. Iterated forcing in quadratic form theory. Israel journal of mathematics, vol. 79 (1992), pp. 297–315. - Otmar Spinas. Cardinal invariants and quadratic forms. Set theory of the reals, edited by Haim Judah, Israel mathematical conference proceedings, vol. 6, Gelbart Research Institute for Mathematical Sciences, Bar-Ilan University, Ramat-Gan 1993, distributed by the American Mathematical Society, Providence, pp. 563–581. - Saharon Shelah and Otmar Spinas. Gross spaces. Transactions of the American Mathematical Society, vol. 348 (1996), pp. 4257–4277.

2001 ◽  
Vol 7 (2) ◽  
pp. 285-286
Author(s):  
Paul C. Eklof
Keyword(s):  
Quadratic Form ◽  
Quadratic Forms ◽  
American Mathematical Society ◽  
Mathematical Society ◽  
Symbolic Logic ◽  
Iterated Forcing ◽  
Independence Result ◽  
Form Theory ◽  
Mathematical Sciences ◽  
Consistency Proofs

Set Theory Generated by Abelian Group Theory

1997 ◽  
Vol 3 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Paul C. Eklof
Keyword(s):  
Group Theory ◽  
Abelian Group ◽  
Set Theory ◽  
Identity Element ◽  
Historical Context ◽  
Group Operation ◽  
Independence Result ◽  
Comprehensive Survey ◽  
New Ideas ◽  
Free Abelian Groups

Introduction. This survey is intended to introduce to logicians some notions, methods and theorems in set theory which arose—largely through the work of Saharon Shelah—out of (successful) attempts to solve problems in abelian group theory, principally the Whitehead problem and the closely related problem of the existence of almost free abelian groups. While Shelah's first independence result regarding the Whitehead problem used established set-theoretical methods (discussed below), his later work required new ideas; it is on these that we focus. We emphasize the nature of the new ideas and the historical context in which they arose, and we do not attempt to give precise technical definitions in all cases, nor to include a comprehensive survey of the algebraic results.In fact, very little algebraic background is needed beyond the definitions of group and group homomorphism. Unless otherwise specified, we will use the word “group” to refer to an abelian group, that is, the group operation is commutative. The group operation will be denoted by +, the identity element by 0, and the inverse of a by −a. We shall use na as an abbreviation for a + a + … + a [n times] if n is positive, and na = (−n)(−a) if n is negative.

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