scholarly journals Constructible Functions on the Steinberg Variety

1997 ◽  
Vol 130 (2) ◽  
pp. 287-310 ◽  
Author(s):  
G. Lusztig
Keyword(s):  
Constructible Functions

scholarly journals Exponential-constructible functions in P-minimal structures

2019 ◽  
Vol 20 (02) ◽  
pp. 2050005
Author(s):  
Saskia Chambille ◽  
Pablo Cubides Kovacsics ◽  
Eva Leenknegt
Keyword(s):  
Skolem Functions ◽  
Constructible Functions ◽  
Stability Results

Exponential-constructible functions are an extension of the class of constructible functions. This extension was formulated by Cluckers and Loeser in the context of semi-algebraic and sub-analytic structures, when they studied stability under integration. In this paper, we will present a natural refinement of their definition that allows for stability results to hold within the wider class of [Formula: see text]-minimal structures. One of the main technical improvements is that we remove the requirement of definable Skolem functions from the proofs. As a result, we obtain stability in particular for all intermediate structures between the semi-algebraic and the sub-analytic languages.

scholarly journals Open-constructible functions

2014 ◽  
Vol 178 ◽  
pp. 453-458
Author(s):  
Alexey Ostrovsky
Keyword(s):  
Constructible Functions

scholarly journals Lebesgue classes and preparation of real constructible functions

2013 ◽  
Vol 264 (7) ◽  
pp. 1599-1642 ◽  
Author(s):  
Raf Cluckers ◽  
Daniel J. Miller
Keyword(s):  
Constructible Functions

scholarly journals INTEGRATION AND CELL DECOMPOSITION IN P-MINIMAL STRUCTURES

2016 ◽  
Vol 81 (3) ◽  
pp. 1124-1141 ◽  
Author(s):  
PABLO CUBIDES KOVACSICS ◽  
EVA LEENKNEGT
Keyword(s):  
Cell Decomposition ◽  
Poincaré Series ◽  
Weak Version ◽  
Poincare Series ◽  
Skolem Functions ◽  
Direct Corollary ◽  
Image Position ◽  
And Function ◽  
Constructible Functions

AbstractWe show that the class of ${\cal L}$-constructible functions is closed under integration for any P-minimal expansion of a p-adic field $\left( {K,{\cal L}} \right)$. This generalizes results previously known for semi-algebraic and subanalytic structures. As part of the proof, we obtain a weak version of cell decomposition and function preparation for P-minimal structures, a result which is independent of the existence of Skolem functions. A direct corollary is that Denef’s results on the rationality of Poincaré series hold in any P-minimal expansion of a p-adic field $\left( {K,{\cal L}} \right)$.

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