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Combinatorial principles in nonstandard analysis

Mauro Di Nasso, Karel Hrbacek
2003 Annals of Pure and Applied Logic  
We study 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.  ... 
doi:10.1016/s0168-0072(02)00059-3 fatcat:f3omqc5wafglbjjp3canb74pyq

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.  ... 

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.  ... 

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  ... 

Page 4054 of Mathematical Reviews Vol. , Issue 97G [page]

1997 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.  ... 

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.  ... 

Page 1307 of Mathematical Reviews Vol. , Issue 96c [page]

1996 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.  ... 

Page 4419 of Mathematical Reviews Vol. , Issue 86j [page]

1986 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.  ... 

Page 4871 of Mathematical Reviews Vol. , Issue 84m [page]

1984 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.  ... 

Book Review: Radically elementary probability theory

Loren D. Pitt
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] .  ... 
doi:10.1090/s0273-0979-1989-15779-0 fatcat:hsvp7uj42ng5pelhjo5qqbb5du

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

Mauro Di Nasso
2016 arXiv   pre-print
By presenting the proofs of a few sample results, we introduce the reader to the use of 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.  ... 
arXiv:1312.5059v2 fatcat:tpfqs7kbdngrbnjou2jcfzr3oi

A taste of nonstandard methods in combinatorics of numbers [chapter]

Mauro Di Nasso
2014 Geometry, Structure and Randomness in Combinatorics  
By presenting the proofs of a few sample results, we introduce the reader to the use of 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.  ... 
doi:10.1007/978-88-7642-525-7_3 fatcat:mjpeqfnnybcrtljg2piqv4y5ly

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.  ... 

Ultrafilters maximal for finite embeddability

Lorenzo Luperi Baglini
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 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.  ... 
doi:10.4115/jla.2014.6.6 fatcat:uh6vhc7zm5fxndlo3np3wgjqze

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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