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On the Spectrum of Characters of Ultrafilters

Shimon Garti, Menachem Magidor, Saharon Shelah
<span title="">2018</span> <i title="Duke University Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/un57kpou5jawnm7yjqoeumbno4" style="color: black;">Notre Dame Journal of Formal Logic</a> </i> &nbsp;
We show that the character spectrum Sp_χ(λ), for a singular cardinal λ of countable cofinality, may include any prescribed set of regular cardinals between λ and 2^λ.  ...  introduction The purpose of this paper is to analize the spectrum of characters of uniform ultrafilters. Recall that an ultrafilter U on λ is called uniform if the size of every member of U is λ.  ...  We need some basic definitions for describing the contents of this paper: Definition 0.1. Characters of ultrafilters. Let λ be an infinite cardinal, and U an ultrafilter on λ.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1215/00294527-2018-0006">doi:10.1215/00294527-2018-0006</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tygit6wlznhabevusruzr6zkoa">fatcat:tygit6wlznhabevusruzr6zkoa</a> </span>
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The spectrum of characters of ultrafilters on omega [article]

Saharon Shelah
<span title="2007-08-15">2007</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We show the consistency of the set of regular cardinals which are the character of some ultrafilter on omega is not convex. We also deal with the set of pi chi-characters of ultrafilters on omega.  ...  the investigation of consistency on χ(D). In §2 we note what we can say on the strict π-character of ultrafilters.  ...  Recall 0.1 Definition. 1) Sp χ = Sp(χ) is the set of cardinals θ such that: θ = χ(D) for some non-principal ultrafilter D on ω where 2) For D an ultrafilter on ω let θ = χ(D) be the minimal cardinality  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/0612240v2">arXiv:math/0612240v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5onlferq7rg33chfilqq4ydmlm">fatcat:5onlferq7rg33chfilqq4ydmlm</a> </span>
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The spectrum of characters of ultrafilters on ω

Saharon Shelah
<span title="">2008</span> <i title="Institute of Mathematics, Polish Academy of Sciences"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qja4hqeadzam7ph6bhaks7ersu" style="color: black;">Colloquium Mathematicum</a> </i> &nbsp;
½µ Sp χ = Sp(χ) × Ø × Ø Ó Ö Ò Ð× θ ×Ù Ø Ø θ = χ(D) ÓÖ ×ÓÑ ÒÓÒ¹ÔÖ Ò Ô Ð ÙÐØÖ ÐØ Ö D ÓÒ ω Û Ö ´¾µ ÓÖ D Ò ÙÐØÖ ÐØ Ö ÓÒ ω Ð Ø θ = χ(D) Ø Ñ Ò Ñ Ð Ö Ò Ð ØÝ θ ×Ù Ø Ø D × Ò Ö Ø Ý ×ÓÑ Ñ ÐÝ Ó θ Ñ Ñ Ö׸ º º Å Ò{|  ...  µ P¹Ò Ñ Ó Ò ÙÐØÖ ÐØ Ö D ÜØ Ò Ò D¸ Ò Û Ú Q(D) ⋖ P * Q(D + )´Ù× ÓÖ Ø Ü ×Ø Ò Ó ÒÓÒ Ð Ð Ñ Øµº ËÙ ÓÖ Ò × ÓÑ Ò Ò Ä Ú Ö ÓÖ Ò Ò Å Ø × ÓÖ Ò ÓÖ Ò ÙÐØÖ ¹ ÐØ Ö D ÓÒ ω¸Ø Ø × p ∈ D p × ×Ù ØÖ Ó ω Û Ø ØÖÙÒ tr(p) ∈ p  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4064/cm111-2-5">doi:10.4064/cm111-2-5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kgukihqzkfdivnwcyhccyfaeum">fatcat:kgukihqzkfdivnwcyhccyfaeum</a> </span>
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SPM Bulletin 30 [article]

Boaz Tsaban
<span title="2010-06-15">2010</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This is the 30th issue of this bulletin, dedicated to mathematical selection principles and related areas. Now in a concise format.  ...  In particular, it is shown that tightness and character coincide for the continuous convergence on C(X, R) and is equal to the Lindelöf degree of X.  ...  We point out one of the differences between rapid ultrafilters and Q-points: Rapid ultrafilters may have empty intersection with van der Waerden ideal, whereas every Q-point has a non-empty intersection  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1006.3023v1">arXiv:1006.3023v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lxntnozuovcqzffmn6776f2ece">fatcat:lxntnozuovcqzffmn6776f2ece</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-1006.3023/1006.3023.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f7/ff/f7ff3b720d50ebdebc5d345205ccd39bc3f41eb4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1006.3023v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

More on uniform ultrafilters over a singular cardinal

Moti Gitik
<span title="">2020</span> <i title="Institute of Mathematics, Polish Academy of Sciences"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/yeobluctzze7rfwekxs7sx2ayy" style="color: black;">Fundamenta Mathematicae</a> </i> &nbsp;
Shelah [6] initiated the study of the character and the ultrafilter number of uniform ultrafilters over a singular cardinal.  ...  We present some new results related to the character of uniform ultrafilters over a singular cardinal and the ultrafilter number. 1. Introduction.  ...  We would like to thank the referee of the paper for his remarks and corrections. The research was partially supported by Israel Science Foundation Grant no. 1216/18.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4064/fm845-5-2020">doi:10.4064/fm845-5-2020</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/boxb6ar5knaqto4krk67fmmb2a">fatcat:boxb6ar5knaqto4krk67fmmb2a</a> </span>
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Page 3432 of Mathematical Reviews Vol. , Issue 88g [page]

<span title="">1988</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
topology; then, to the real spectrum of the coordinate ring A of M (denoted #-Spec A), which is viewed as the ultrafilter completion of M(R) and in which also live the orders on R(M); finally, back to  ...  This answers a question of Weil and Serre. Using Fourier transform, the author produces a vector space over Q,; on which the Galois group acts, with character equal to the Artin character.  ... 
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Spectra of Tukey types of ultrafilters on Boolean algebras [article]

Jennifer A. Brown, Natasha Dobrinen
<span title="2015-03-18">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Extending recent investigations on the structure of Tukey types of ultrafilters on P(ω) to Boolean algebras in general, we classify the spectra of Tukey types of ultrafilters for several classes of Boolean  ...  H C = {(T ↑ t) \ s∈S (T ↑ s) : t ∈ C, The character χ of an ultrafilter U on Treealg T is the minimum size of a generating set for U.  ...  Thus, for each infinite cardinal κ, the spectrum of the Tukey types of ultrafilters on Remark.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1406.2084v2">arXiv:1406.2084v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/k5oavoongfbczlblipc4u7nmwe">fatcat:k5oavoongfbczlblipc4u7nmwe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20191016233547/https://arxiv.org/pdf/1406.2084v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/98/55/9855ea382eae98b6aaeb3ea7955b0ee00edea951.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1406.2084v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Page 1889 of Mathematical Reviews Vol. , Issue 91D [page]

<span title="">1991</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
theorem.” 91d:15003 15A04 34430 Laitochova, Jitka (CS-PLCK) On two-dimensional linear spaces of continuous functions of the same character.  ...  strongly regular spaces of continuous functions is that the spaces must have the same character.  ... 
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:{unav)

Saharon Shelah, Jörg Brendle, Saharon Shelah
<span title="2018-12-31">2018</span> <i title="American Mathematical Society (AMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/w3g32txdvneltemssag5nwfxcy" style="color: black;">Transactions of the American Mathematical Society</a> </i> &nbsp;
For a free ultrafilter U on ω we study several cardinal characteristics which describe part of the combinatorial structure of U .  ...  We also investigate two ideals on the Baire space ω ω naturally related to U and calculate cardinal coefficients of these ideals in terms of cardinal characteristics of the underlying ultrafilter.  ...  To this end we define • Spec(χ) = {λ; χ(U) = λ for some ultrafilter U on ω}, the character spectrum; • Spec(πχ) = {λ; πχ(U) = λ for some ultrafilter U on ω}, the π-character spectrum; • Spec (χ) = {λ;  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0002-9947-99-02257-6">doi:10.1090/s0002-9947-99-02257-6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rj5ava2yljgmnmt7r7msyakdoa">fatcat:rj5ava2yljgmnmt7r7msyakdoa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190430153618/https://www.ams.org/journals/tran/1999-351-07/S0002-9947-99-02257-6/S0002-9947-99-02257-6.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ea/4e/ea4ee47440f06a44ed6656f569c33d44ff20b67d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0002-9947-99-02257-6"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Inverse semigroups associated with labelled spaces and their tight spectra [article]

Giuliano Boava, Gilles de Castro, Fernando de L. Mortari
<span title="2015-05-26">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Motivated by Exel's work on inverse semigroups and combinatorial C*-algebras, we associate each weakly left resolving labelled space with an inverse semigroup, and characterize the tight spectrum of the  ...  latter in a way that is reminiscent of the description of the boundary path space of a directed graph.  ...  A natural candidate for a topological space for the inverse semigroup to act on is the set of characters defined on the idempotents of the semigroup; however, the C*-algebra constructed from the groupoid  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1505.07123v1">arXiv:1505.07123v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pnczln3jlvdvtm7xznspobc5we">fatcat:pnczln3jlvdvtm7xznspobc5we</a> </span>
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A note on a paper of E. Boasso and A. Larotonda: "A spectral theory for solvable Lie algebras of operators"

C. Ott
<span title="1996-03-01">1996</span> <i title="Mathematical Sciences Publishers"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/7bfevq4qbjckrhwmr4edm6npze" style="color: black;">Pacific Journal of Mathematics</a> </i> &nbsp;
In this paper we prove the projection property of this generalized Taylor spectrum with the help of the projection property of the approximate point spectrum.  ...  recently introduced a spectrum for complex solvable Lie algebras of operators, which agrees in the abelian case with the Taylor spectrum for several commuting operators, and proved that their spectrum  ...  Manuscripts must be prepared in accordance with the instructions provided on the inside back cover.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2140/pjm.1996.173.173">doi:10.2140/pjm.1996.173.173</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xlihv5ytyjakddol5dsm5xk4d4">fatcat:xlihv5ytyjakddol5dsm5xk4d4</a> </span>
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Spectra of Tukey types of ultrafilters on Boolean algebras

Jennifer A. Brown, Natasha Dobrinen
<span title="2016-03-23">2016</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3g7sk2fqarhcrmieipwvp62bfe" style="color: black;">Algebra Universalis</a> </i> &nbsp;
Extending recent investigations on the structure of Tukey types of ultrafilters on P(ω) to Boolean algebras in general, we classify the spectra of Tukey types of ultrafilters for several classes of Boolean  ...  We also give conditions guaranteeing the existence of an ultrafilter of maximum Tukey type, and show that each free algebra has exactly one Tukey type, the maximum.  ...  By the Tukey spectrum of a Boolean algebra B, denoted Ts(B), we mean the set of all Tukey types of all ultrafilters on B; this is exactly the structure of the Tukey types of ultrafilters on B.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00012-016-0379-y">doi:10.1007/s00012-016-0379-y</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wyyidgr3zrcw5eukcaouzq2f7a">fatcat:wyyidgr3zrcw5eukcaouzq2f7a</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170922004931/http://web.cs.du.edu/dobrinen/BrownDobrinen_TukeySpectra_30May_formatted.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/97/db/97db8e12776b364f82ae4b981c1307d28d7c8ace.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00012-016-0379-y"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Page 1651 of Mathematical Reviews Vol. , Issue 90C [page]

<span title="">1990</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
In The- orem 4, the author uses a version of Baumgartner’s strengthening of MA with CH to establish a similar conclusion (based on X;- sequences rather than on No-sequences) for topological groups of character  ...  Then the author studies the spectrum of compactness and the degree of compactness of an f-set. Theorem 3.11: Let (X,2) be the product of a family of f.t.s.  ... 
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Ultrafilters on omega --- their ideals and their cardinal characteristics [article]

Jörg Brendle, Saharon Shelah
<span title="1997-10-15">1997</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
For a free ultrafilter U on omega we study several cardinal characteristics which describe part of the combinatorial structure of U.  ...  We also investigate two ideals on the Baire space omega^omega naturally related to U and calculate cardinal coefficients of these ideals in terms of cardinal characteristics of the underlying ultrafilter  ...  To this end we define • Spec(χ) = {λ; χ(U) = λ for some ultrafilter U on ω}, the character spectrum; • Spec(πχ) = {λ; πχ(U) = λ for some ultrafilter U on ω}, the π-character spectrum; • Spec ⋆ (χ) = {λ  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/9710217v1">arXiv:math/9710217v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/efk75tcbtrcpbeg5ppt3sak5dm">fatcat:efk75tcbtrcpbeg5ppt3sak5dm</a> </span>
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Representations of the direct product of matrix algebras

Daniele Guido, Lars Tuset
<span title="">2001</span> <i title="Institute of Mathematics, Polish Academy of Sciences"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/yeobluctzze7rfwekxs7sx2ayy" style="color: black;">Fundamenta Mathematicae</a> </i> &nbsp;
A bijection is set up between the equivalence classes of irreducible representations of B as operators on a Banach space and the σ-complete ultrafilters on X (Theorem 2.6).  ...  Therefore, if X has less than measurable cardinality (e.g. accessible), the equivalence classes of the irreducible representations of B are labeled by points of X, and all representations of B are described  ...  We also thank the referee for calling our attention to reference [1] .  ... 
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