Zobrazeno 1 - 10
of 72
pro vyhledávání: '"Mauro Di Nasso"'
Publikováno v:
Boletim da Sociedade Paranaense de Matemática, Vol 20, Iss 1-2, Pp 9-20 (2002)
We introduce the notion of Hausdorff extension of an arbitrary set Xand we study the connections with the Stone-Cech compactification beta X of the discrete space X. We characterize those Hausdorff extensions that satisfy the “transfer principle”
Externí odkaz:
https://doaj.org/article/94a5e345517c4e65ba92d1c9dca35970
Autor:
Mauro Di Nasso
We show the existence of several infinite monochromatic patterns in the integers obtained as values of suitable symmetric polynomials. The simplest example is the following. For every finite coloring of the natural numbers $\mathbb{N}=C_1\cup\ldots\c
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::59802b7c8a77e4e9e7c91c2b04865714
http://hdl.handle.net/11568/1132544
http://hdl.handle.net/11568/1132544
Autor:
Mauro Di Nasso, Eleftherios Tachtsis
Publikováno v:
Proceedings of the American Mathematical Society. 146:397-411
We introduce the notion of additive filter and present a new proof of the existence of idempotent ultrafilters on N without any use of Zorn's Lemma, and where one only assumes the Ultrafilter Theorem for the continuum.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d31f60e20370359c7287c8b0f50fe06e
https://doi.org/10.1090/proc/13719
https://doi.org/10.1090/proc/13719
Autor:
Mauro Di Nasso
Publikováno v:
Combinatorial and Additive Number Theory III ISBN: 9783030311056
We present a self-contained proof of a strong version of van der Waerden’s Theorem. By using translation invariant filters that are maximal with respect to inclusion, a simple inductive argument shows the existence of “piecewise syndetically”-m
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fc7b0b931041b2bfa40aea1a44a36f61
https://doi.org/10.1007/978-3-030-31106-3_6
https://doi.org/10.1007/978-3-030-31106-3_6
Publikováno v:
Lecture Notes in Mathematics ISBN: 9783030179557
Lecture Notes in Mathematics
Lecture Notes in Mathematics
Part I Preliminaries. - Ultrafilters. - Nonstandard Analysis. - Hyperfinite Generators of Ultrafilters. - Many Stars: Iterated Nonstandard Extensions. - LoebMeasure. - Part II Ramsey Theory. - Ramsey's Theorem. - The Theorems of van der Waerden and H
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::69fce464f84b7a02cd91bf71f0349e84
https://doi.org/10.1007/978-3-030-17956-4
https://doi.org/10.1007/978-3-030-17956-4
Publikováno v:
Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory ISBN: 9783030179557
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::28e45f7263c0dbfefe3112eb4bb9449b
https://doi.org/10.1007/978-3-030-17956-4_17
https://doi.org/10.1007/978-3-030-17956-4_17
Autor:
Mauro Di Nasso, Vieri Benci
Publikováno v:
How to Measure the Infinite: Numerosities and Nonstandard Analysis
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e435f021248bff107a0b6bbdec50ded1
http://hdl.handle.net/11568/991469
http://hdl.handle.net/11568/991469
Publikováno v:
Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory ISBN: 9783030179557
In this chapter, we will show that there is a very tight connection between ultrafilters (introduced in Chap. 1) and nonstandard methods (introduced in Chap. 2). Indeed, any element (or “point”) in a nonstandard extension gives rise to an ultrafi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f6b191bf1b0fef340c2c1b53cde6cb0e
https://doi.org/10.1007/978-3-030-17956-4_3
https://doi.org/10.1007/978-3-030-17956-4_3
Publikováno v:
Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory ISBN: 9783030179557
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f6a64bd17cd645398e27aacbdd1a55b6
https://doi.org/10.1007/978-3-030-17956-4_5
https://doi.org/10.1007/978-3-030-17956-4_5
Publikováno v:
Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory ISBN: 9783030179557
In this section, we discuss a conjecture of Erdős, which states that a set of natural numbers of positive lower density contains the sum of two infinite sets. We begin with the history of the conjecture and discuss its nonstandard reformulation. We
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::544e519e32360f14cfd915a633117db8
https://doi.org/10.1007/978-3-030-17956-4_13
https://doi.org/10.1007/978-3-030-17956-4_13