On the regular extension axiom and its variants

2003 ◽  
Vol 49 (5) ◽  
pp. 511-518 ◽  
Author(s):  
Michael Rathjen ◽  
Robert S. Lubarsky
Keyword(s):  
Regular Extension ◽  
Extension Axiom

The disjunction and related properties for constructive Zermelo-Fraenkel set theory

2005 ◽  
Vol 70 (4) ◽  
pp. 1233-1254 ◽  
Author(s):  
Michael Rathjen
Keyword(s):  
Set Theory ◽  
Proof Technique ◽  
Disjunction Property ◽  
Regular Extension ◽  
Existence Property ◽  
Extension Axiom

AbstractThis paper proves that the disjunction property, the numerical existence property. Church's rule, and several other metamathematical properties hold true for Constructive Zermelo-Fraenkel Set Theory, CZF, and also for the theory CZF augmented by the Regular Extension Axiom.As regards the proof technique, it features a self-validating semantics for CZF that combines realizability for extensional set theory and truth.

Generalized geometric theories and set-generated classes

2014 ◽  
Vol 25 (7) ◽  
pp. 1466-1483 ◽  
Author(s):  
PETER ACZEL ◽  
HAJIME ISHIHARA ◽  
TAKAKO NEMOTO ◽  
YASUSHI SANGU
Keyword(s):  
Set Theory ◽  
Special Form ◽  
Geometric Theory ◽  
Regular Extension ◽  
Additional Axiom ◽  
Extension Axiom ◽  
Propositional Theory ◽  
Dependent Choice ◽  
Formal Topology

We introduce infinitary propositional theories over a set and their models which are subsets of the set, and define a generalized geometric theory as an infinitary propositional theory of a special form. The main result is thatthe class of models of a generalized geometric theory is set-generated. Here, a class$\mathcal{X}$of subsets of a set is set-generated if there exists a subsetGof$\mathcal{X}$such that for each α ∈$\mathcal{X}$, and finitely enumerable subset τ of α there exists a subset β ∈Gsuch that τ ⊆ β ⊆ α. We show the main result in the constructive Zermelo–Fraenkel set theory (CZF) with an additional axiom, called the set generation axiom which is derivable inCZF, both from the relativized dependent choice scheme and from a regular extension axiom. We give some applications of the main result to algebra, topology and formal topology.

scholarly journals Bounded realization of l-groups over global fields

1998 ◽  
Vol 150 ◽  
pp. 13-62 ◽  
Author(s):  
Wulf-Dieter Geyer ◽  
Moshe Jarden
Keyword(s):  
Finite Field ◽  
Prime Number ◽  
Finite Fields ◽  
Galois Extension ◽  
Prime Ideals ◽  
Transfer Principle ◽  
Global Fields ◽  
Regular Extension ◽  
Root Of Unity ◽  
Result Theorem

Abstract.We use the method of Scholz and Reichardt and a transfer principle from finite fields to pseudo finite fields in order to prove the following result. THEOREM Let G be a group of order ln, where l is a prime number. Let K0be either a finite field with |K0| > l4n+4or a pseudo finite field. Suppose that l ≠ char(K0) and that K0does not contain the root of unity ζl of order l. Let K = K0(t), with t transcendental over K0. Then K has a Galois extension L with the following properties: (a) (L/K) ≅ G; (b) L/K0is a regular extension; (c) genus(L) < ; (d) K0[t] has exactly n prime ideals which ramify in L; the degree of each of them is [K0: K0]; (e) (t)∞totally decomposes in L; (f) L = K(x), withand deg(ai(t)) < deg(a1(t)) for i = 1,…,ln.

OnK 0-functions and regular extension operators

1992 ◽  
Vol 59 (3) ◽  
pp. 272-275 ◽  
Author(s):  
Jose L. Blasco
Keyword(s):  
Regular Extension

scholarly journals REB’s statistical series: surveys of industrial enterprises

2021 ◽  
pp. 15-45
Author(s):  
S. Aukutsionek ◽  
A. Batyaeva ◽  
N. Dyomina ◽  
A. Egorov ◽  
A. Matveev
Keyword(s):  
Comparative Analysis ◽  
Statistical Data ◽  
Economic Indicators ◽  
Regular Extension ◽  
Industrial Enterprises ◽  
Statistical Series ◽  
Wide Range

Industrial indexes of the Russian Economic Barometer cover a wide range of economic indicators of Russia’s industrial enterprises. The article presents the basic statistical data collected on a monthly, quarterly and semi-annual base by the Russian Economic Barometer through direct surveys of industrial enterprises’ managers. Regular extension of rows allows to consider the dynamics of more than 100 series of indicators, to conduct a comparative analysis of data collected since 1991.

scholarly journals REB’s statistical series: surveys of industrial enterprises

2021 ◽  
pp. 24-55
Author(s):  
S. Aukutsionek ◽  
A. Batyaeva ◽  
N. Dyomina ◽  
A. Egorov ◽  
A. Matveev
Keyword(s):  
Comparative Analysis ◽  
Statistical Data ◽  
Economic Indicators ◽  
Regular Extension ◽  
Industrial Enterprises ◽  
Statistical Series ◽  
Wide Range

Industrial indexes of the Russian Economic Barometer cover a wide range of economic indicators of Russia’s industrial enterprises. The article presents the basic statistical data collected on a monthly, quarterly and semi-annual base by the Russian Economic Barometer through direct surveys of industrial enterprises’ managers. Regular extension of rows allows to consider the dynamics of more than 100 series of indicators, to conduct a comparative analysis of data collected since 1991.

scholarly journals REB’s statistical series: surveys of industrial enterprises

2021 ◽  
pp. 22-53
Author(s):  
S. Aukutsionek ◽  
A. Batyaeva ◽  
N. Dyomina ◽  
A. Egorov ◽  
A. Matveev
Keyword(s):  
Comparative Analysis ◽  
Statistical Data ◽  
Economic Indicators ◽  
Regular Extension ◽  
Industrial Enterprises ◽  
Statistical Series ◽  
Wide Range

Industrial indexes of the Russian Economic Barometer cover a wide range of economic indicators of Russia’s industrial enterprises. The article presents the basic statistical data collected on a monthly, quarterly and semi-annual base by the Russian Economic Barometer through direct surveys of industrial enterprises’ managers. Regular extension of rows allows to consider the dynamics of more than 100 series of indicators, to conduct a comparative analysis of data collected since 1991.

scholarly journals REB’s statistical series: surveys of industrial enterprises

2020 ◽  
pp. 23-54
Author(s):  
S. Aukutsionek ◽  
A. Batyaeva ◽  
N. Dyomina ◽  
A. Egorov ◽  
A. Matveev
Keyword(s):  
Comparative Analysis ◽  
Statistical Data ◽  
Economic Indicators ◽  
Regular Extension ◽  
Industrial Enterprises ◽  
Statistical Series ◽  
Wide Range

Industrial indexes of the Russian Economic Barometer cover a wide range of economic indicators of Russia’s industrial enterprises. The article presents the basic statistical data collected on a monthly, quarterly and semi-annual base by the Russian Economic Barometer through direct surveys of industrial enterprises managers. Regular extension of rows allows to consider the dynamics of more than 100 series of indicators, to conduct a comparative analysis of data collected since 1991.

scholarly journals REB’s statistical series: surveys of industrial enterprises

2021 ◽  
pp. 14-45
Author(s):  
S. Aukutsionek ◽  
A. Batyaeva ◽  
N. Dyomina ◽  
A. Egorov ◽  
A. Matveev
Keyword(s):  
Comparative Analysis ◽  
Statistical Data ◽  
Economic Indicators ◽  
Regular Extension ◽  
Industrial Enterprises ◽  
Statistical Series ◽  
Wide Range

Industrial indexes of the Russian Economic Barometer cover a wide range of economic indicators of Russia’s industrial enterprises. The article presents the basic statistical data collected on a monthly, quarterly and semi-annual base by the Russian Economic Barometer through direct surveys of industrial enterprises’ managers. Regular extension of rows allows to consider the dynamics of more than 100 series of indicators, to conduct a comparative analysis of data collected since 1991.

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