About the some conditions of the replaceability of the double induction

The provability of the axiom of double induction (ADI) with the open induction formula in the additive arithmetic is investigated. The system of additional axioms and theirs provability by ADI is presented.

The Multi-Dimensional Local Theorem for Additive Arithmetic Functions

Analytic and Probabilistic Methods in Number Theory ◽

10.1515/9783112314234-029 ◽

1992 ◽

pp. 285-292

Keyword(s):

Arithmetic Functions ◽

Additive Arithmetic ◽

Local Theorem

Open induction

The Notre Dame Lectures ◽

10.1201/9781439865743-41 ◽

2005 ◽

pp. 158-159

Keyword(s):

Open Induction and the True Theory of Rationals

Journal of Symbolic Logic ◽

10.2307/2274365 ◽

1987 ◽

Vol 52 (3) ◽

pp. 793 ◽

Cited By ~ 2

Author(s):

Zofia Adamowicz

Keyword(s):

True Theory ◽

Corrigendum: On Diophantine Equations Solvable in Models of Open Induction.

Journal of Symbolic Logic ◽

10.2307/2275050 ◽

1991 ◽

Vol 56 (3) ◽

pp. 811

Author(s):

Margarita Otero

Keyword(s):

Diophantine Equations ◽

Grundlehren der mathematischen Wissenschaften - Arithmetic Functions and Integer Products ◽

Additive Arithmetic Functions on Differences

10.1007/978-1-4613-8548-6_11 ◽

1985 ◽

pp. 204-243

Author(s):

P. D. T. A. Elliott

Keyword(s):

Arithmetic Functions ◽

The amalgamation property in normal open induction.

Notre Dame Journal of Formal Logic ◽

10.1305/ndjfl/1093634563 ◽

1992 ◽

Vol 34 (1) ◽

pp. 50-55 ◽

Cited By ~ 1

Author(s):

Margarita Otero

Keyword(s):

Amalgamation Property ◽

Open induction in a bounded arithmetic for TC0

Archive for Mathematical Logic ◽

10.1007/s00153-014-0414-7 ◽

2014 ◽

Vol 54 (3-4) ◽

pp. 359-394

Author(s):

Emil Jeřábek

Keyword(s):

Bounded Arithmetic ◽

Distribution of additive arithmetic functions with shifted arguments. II

Lithuanian Mathematical Journal ◽

10.1007/bf00966422 ◽

1982 ◽

Vol 22 (3) ◽

pp. 294-302

Author(s):

Z. Kryžius

Keyword(s):

Arithmetic Functions ◽

On the limiting distribution of additive arithmetic functions

Acta Mathematica ◽

10.1007/bf02392108 ◽

1974 ◽

Vol 132 (0) ◽

pp. 53-75 ◽

Cited By ~ 4

Author(s):

P. D. T. A. Elliott

Keyword(s):

Limiting Distribution ◽

Arithmetic Functions ◽

Distribution of a class of additive arithmetic functions with values in a Hilbert space

Lithuanian Mathematical Journal ◽

10.1007/bf00968332 ◽

1986 ◽

Vol 25 (4) ◽

pp. 352-359

Author(s):

V. Nakutis

Keyword(s):

Hilbert Space ◽

Arithmetic Functions ◽