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Combinatorial principles in nonstandard analysis

2003
*
Annals of Pure and Applied Logic
*

We study

doi:10.1016/s0168-0072(02)00059-3
fatcat:f3omqc5wafglbjjp3canb74pyq
*combinatorial**principles*related to the Isomorphism Property and the Special Model Axiom*in**nonstandard**analysis*. 1991 Mathematics Subject Classification. 03H05, 03C62, 03C50, 26E35. ...*nonstandard**analysis*. ... It also makes the*principles*less attractive to those practitioners of*nonstandard**analysis*who are not logicians. ...##
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Page 3802 of Mathematical Reviews Vol. , Issue 2002F
[page]

2002
*
Mathematical Reviews
*

property

*in**nonstandard**analysis*. ... The author presents two infinitary,*combinatorial**principles*Aj and A;, from which he derives a number of results*in*non-standard*analysis*. ...##
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Page 8928 of Mathematical Reviews Vol. , Issue 2003m
[page]

2003
*
Mathematical Reviews
*

*principles*

*in*

*nonstandard*

*analysis*. ... This article deals with

*combinatorial*

*principles*related to the so- called isomorphism property. This last property is a strengthening of the «-saturation often used

*in*

*nonstandard*

*analysis*. ...

##
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Page 3951 of Mathematical Reviews Vol. , Issue 88h
[page]

1988
*
Mathematical Reviews
*

The authors study two

*combinatorial**principles*T(Z,,) [resp. ... The author shows that the*principles*of intuitionistic*analysis*(*in*particular Kripke’s scheme, the axiom of choice, bar induction and the continuity*principle*) are preserved under glueing their models ...##
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Page 4054 of Mathematical Reviews Vol. , Issue 97G
[page]

1997
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Mathematical Reviews
*

The opening tutorial explains the general

*principles*of*nonstandard**analysis**in*terms of E. ... This book is an introductory survey of*nonstandard**analysis*as practiced*in*the French school founded by Georges Reeb. ...##
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Page 1991 of Mathematical Reviews Vol. , Issue 90D
[page]

1990
*
Mathematical Reviews
*

The reader is expected to be already familiar with the terminology of

*nonstandard**analysis*. N. ...*In*this paper some standard results*in*Ramsey theory are proved using the methods of*nonstandard**analysis*. The paper is well written and some nice motivational examples are included. ...##
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Page 1307 of Mathematical Reviews Vol. , Issue 96c
[page]

1996
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Mathematical Reviews
*

(RS-AOSSI; Novosibirsk)

*Nonstandard**analysis*and the axiom of determinacy. (Russian. ... The authors develop a*nonstandard*theory of hereditarily finite sets (replacing the axiom of infinity*in*ZF by its negation), suitable for classical*analysis*. ...##
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Page 4419 of Mathematical Reviews Vol. , Issue 86j
[page]

1986
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Mathematical Reviews
*

E.
(3-CONC)
On the plausibility of

*nonstandard*proofs*in**analysis*. (French and German summaries) Dialectica 38 (1984), no. 4, 297-310. ... (Russian)*Combinatorial*-algebraic methods*in*applied mathematics, 48-56, 121, Gor’kov. Gos. Univ., Gorki, 1979. ...##
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Page 4871 of Mathematical Reviews Vol. , Issue 84m
[page]

1984
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Mathematical Reviews
*

Among the properties of Eff are the following: (1) the statements of (Heyting) arithmetic holding

*in*Eff are those realized*in*Kleene’s sense; (2) real*analysis*is*in*Markov’s sense (and the latter’s*principle*... M.(3-WTRL-B) **Combinatorial*enumeration. With a foreword by Gian-Carlo Rota. Wiley-Interscience Series*in*Discrete Mathematics. A Wiley-Interscience Publication. ...##
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Book Review: Radically elementary probability theory

1989
*
Bulletin of the American Mathematical Society
*

*Nonstandard*

*analysis*was created by Abraham Robinson

*in*1960 to lay a rigorous foundation for infinitesimals

*in*

*analysis*. ...

*In*1977 Nelson published an alternative

*nonstandard*

*analysis*which he called internal set theory or 1ST [7] . ...

##
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A taste of nonstandard methods in combinatorics of numbers
[article]

2016
*
arXiv
*
pre-print

By presenting the proofs of a few sample results, we introduce the reader to the use of

arXiv:1312.5059v2
fatcat:tpfqs7kbdngrbnjou2jcfzr3oi
*nonstandard**analysis**in*aspects of combinatorics of numbers. ... Introduction*In*the last years, several*combinatorial*results about sets of integers that depend on their asymptotic densities have been proved by using the techniques of*nonstandard**analysis*, starting ... More generally,*in**nonstandard**analysis*one considers hyper-extensions of arbitrary sets and functions. ...##
###
A taste of nonstandard methods in combinatorics of numbers
[chapter]

2014
*
Geometry, Structure and Randomness in Combinatorics
*

By presenting the proofs of a few sample results, we introduce the reader to the use of

doi:10.1007/978-88-7642-525-7_3
fatcat:mjpeqfnnybcrtljg2piqv4y5ly
*nonstandard**analysis**in*aspects of combinatorics of numbers. 2000 Mathematics Subject Classification. 03H05; 11B05 ... Introduction*In*the last years, several*combinatorial*results about sets of integers that depend on their asymptotic density have been proved by using the techniques of*nonstandard**analysis*, starting from ... More generally,*in**nonstandard**analysis*one considers hyper-extensions of arbitrary sets and functions. ...##
###
Page 1743 of Mathematical Reviews Vol. 50, Issue 6
[page]

1975
*
Mathematical Reviews
*

The standard

*combinatorial*separation*principles*(generalizations of Ramsey’s theorem) often used*in*evaluating Hanf numbers were inadequate here, and so the authors present a new*combinatorial*lemma, ... Ward f 12713 The isomorphism property*in**nonstandard**analysis*and its use*in*the theory of Banach spaces. J. Symbolic Logic 39 (1974), 717-731. ...##
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Ultrafilters maximal for finite embeddability

2014
*
Journal of Logic and Analysis
*

We refer to Hindman and Strauss [6] for all the notions about combinatorics and ultrafilters that we will use, to Chang and Keisler [3, §4.4] for the foundational aspects of

doi:10.4115/jla.2014.6.6
fatcat:uh6vhc7zm5fxndlo3np3wgjqze
*nonstandard**analysis*and to ...*In*section 4 we reprove our main result by*nonstandard*methods; nevertheless, this is the only section*in*which*nonstandard*methods are used, so the rest of the paper is accessible also to readers unfamiliar ...*In*particular, we will use the notions of*nonstandard*extension of subsets of N and the transfer*principle*. ...##
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Page 1749 of Mathematical Reviews Vol. , Issue 93c
[page]

1993
*
Mathematical Reviews
*

Mathematical Foundations of Computer Science, 16th International, MFCS ’91 Relations between Fundamental Sequences of Ordinal Numbers and

*Combinatorial**Principles*Theoretical Aspects of Computer Science ... 1991: Jean-Michel Members elected to the Academy*in*1991: Michael-Robert Miniconference: Sequential Statistical*Analysis*, SSA Modern sequential*analysis*, SSA, Vol. 2 Montpellier, 1989 NATO Advanced Study ...
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