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Forcing axioms, approachability, and stationary set reflection [article]

Sean D. Cox
<span title="2020-01-09">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We prove a variety of theorems about stationary set reflection and concepts related to internal approachability.  ...  We prove that an implication of Fuchino-Usuba relating stationary reflection to a version of Strong Chang's Conjecture cannot be reversed; strengthen and simplify some results of Krueger about forcing  ...  Separation of stationary set reflection In this section we prove the various separations of stationary reflection from the introduction.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1807.06129v3">arXiv:1807.06129v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wo7ath4exfddbc6wswfght3axu">fatcat:wo7ath4exfddbc6wswfght3axu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200321080506/https://arxiv.org/pdf/1807.06129v3.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] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1807.06129v3" 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>

On reflection of stationary sets

Q. Feng, Menachem Magidor
<span title="">1992</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;
On reflection of stationary sets by Qi F e n g (Singapore) and Menachem M a g i d o r (Jerusalem) Abstract. We show that there are stationary subsets of uncountable spaces which do not reflect.  ...  There are many useful and interesting stationary reflection principles formulated and studied in the current research concerning new existence axioms of set theory and combinatorial aspects of infinity  ...  It is known that the following reflection principle is consistent and has large cardinal aspects. Suppose κ ≥ ω 2 and S ⊆ [H κ ] ω is stationary.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4064/fm-140-2-175-181">doi:10.4064/fm-140-2-175-181</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2j673zkmzvcifd3gvx7yr2jmoy">fatcat:2j673zkmzvcifd3gvx7yr2jmoy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180723090933/http://matwbn.icm.edu.pl/ksiazki/fm/fm140/fm14025.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/16/d2/16d2c14da89b14dca4d5b5c371946815490d9843.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4064/fm-140-2-175-181"> <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>

On reflection of stationary sets in P_kappa lambda [article]

Thomas Jech, Saharon Shelah
<span title="1998-08-24">1998</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We investigate reflection of stationary sets in P_kappa lambda and prove a consistency result for the case when lambda is the successor of kappa.  ...  A stationary set S ⊆ P κ λ reflects at a if the set S ∩ P κ a a is a stationary set in P κ a a. The question underlying our investigation is to what extent can stationary sets reflect.  ...  We are concerned with reflection of stationary sets. Reflection properties of stationary sets of ordinals have been extensively studied, starting with [7] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/9801078v2">arXiv:math/9801078v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/g2ziiadqvve5tnit4idcn2uoi4">fatcat:g2ziiadqvve5tnit4idcn2uoi4</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-math9801078/math9801078.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/f0/9a/f09a256a5643f61812aa57fbeccd2fd9d31d390a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/9801078v2" 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>

Projective Stationary Sets and Strong Reflection Principle [article]

Qi Feng, Thomas Jech
<span title="1994-09-02">1994</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We study projective stationary sets. The Projective Stationary Reflection principle is the statement that every projective stationary set contains an increasing continuous ∈--chain of length ω_1.  ...  We show that if Martin's Maximum holds, then the Projective Stationary Reflection Principle holds. Also it is equivalent to the Strong Reflection Principle.  ...  It differs from the known stationary reflection principles in two respects. First, it is not applicable to every stationary set, but the projective stationary sets.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/9409202v1">arXiv:math/9409202v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xcrqtamprrd2lnkajxzfmdfhyi">fatcat:xcrqtamprrd2lnkajxzfmdfhyi</a> </span>
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Full reflection of stationary sets below aleph_omega [article]

Thomas Jech, Saharon Shelah
<span title="1990-01-15">1990</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
It is consistent that for every n >= 2, every stationary subset of omega_n consisting of ordinals of cofinality omega_k where k = 0 or k <= n-3 reflects fully in the set of ordinals of cofinality omega_n  ...  There exist stationary sets S ⊂ S 3 0 and A ⊂ S 3 1 such that S does not reflect at any γ ∈ A. Proof.  ...  In this paper we investigate the question which stationary subsets of ω n reflect fully in which stationary sets; in other words the structure of the well founded relation <.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/9201242v1">arXiv:math/9201242v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/s4tiah2is5h3xas6zud54nmqlm">fatcat:s4tiah2is5h3xas6zud54nmqlm</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-math9201242/math9201242.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] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/9201242v1" 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>

Possible Behaviours of the Reflection Ordering of Stationary Sets [article]

Jiří Witzany
<span title="1993-09-16">1993</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
If S,T are stationary subsets of a regular uncountable cardinal κ, we say that S reflects fully in T, S<T, if for almost all α∈ T (except a nonstationary set) S ∩α is stationary in α .  ...  We say that a given poset P is realized by the reflection ordering if there is a maximal antichain 〈 X_p ; p ∈ P 〉 of stationary subsets of Reg(κ) so that ∀ p,q ∈ P ∀ S⊆ X_p, T⊆ X_q stationary:(S<T p<_  ...  Reflection of stationary sets in the generic extension. Let us analyze the behaviour of the reflection ordering of stationary subsets of λ in the generic extension V (P λ+1 ).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/9309209v1">arXiv:math/9309209v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jblcstgg25fjplofx4kcgfseay">fatcat:jblcstgg25fjplofx4kcgfseay</a> </span>
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Full reflection of stationary sets at regular cardinals [article]

Thomas Jech, Saharon Shelah
<span title="1992-04-15">1992</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
A stationary subset S of a regular uncountable cardinal kappa reflects fully at regular cardinals if for every stationary set T subseteq kappa of higher order consisting of regular cardinals there exists  ...  We prove that the Axiom of Full Reflection which states that every stationary set reflects fully at regular cardinals, together with the existence of n-Mahlo cardinals is equiconsistent with the existence  ...  In other words, if for all stationary sets T of regular cardinals, o(S) < o(T ) implies S < T. Axiom of Full Reflection for κ. Every stationary subset of κ reflects fully at regular cardinals.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/9204218v1">arXiv:math/9204218v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ceydciiopfaizlqzjxn677ef74">fatcat:ceydciiopfaizlqzjxn677ef74</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-math9204218/math9204218.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/15/da/15dae8ae7649a0b3471ab7eba90164425c6e6ae7.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/9204218v1" 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>

The proper forcing axiom and stationary set reflection

Robert Beaudoin
<span title="1991-05-01">1991</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;
A stationary set S on a cardinal K reflects if there is a limit a <κ with cf a > ω such that SΠa is stationary in a we shall say S reflects at a.  ...  Let us call a family F of stationary sets on K mutually reflecting if for some limit a < K every S e F reflects at a otherwise we call F mutually nonreflecting.  ...  Question: For which m < 2 does MM imply that every family of m stationary subsets of SQ is mutually reflecting?  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2140/pjm.1991.149.13">doi:10.2140/pjm.1991.149.13</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/k2faeeosezc2diyluhoznzcomq">fatcat:k2faeeosezc2diyluhoznzcomq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180724045319/https://msp.org/pjm/1991/149-1/pjm-v149-n1-p02-s.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/c3/a7/c3a78c44667ff864d38a6705eff62d272e5508c4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2140/pjm.1991.149.13"> <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>

Full Reflection of Stationary Sets at Regular Cardinals

Thomas Jech, Saharon Shelah
<span title="">1993</span> <i title="JSTOR"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xkzouzjw7zaljamw6gqar2a3di" style="color: black;">American Journal of Mathematics</a> </i> &nbsp;
It has been proved [7], [3] that reflection of stationary sets is a large cardinal property. We address the question of what is the largest possible amount of reflection.  ...  A stationary subset S of a regular uncountable cardinal κ reflects fully at regular cardinals if for every stationary set T ⊆ κ of higher order consisting of regular cardinals there exists an α ∈ T such  ...  In other words, if for all stationary sets T of regular cardinals, o(S) < o(T ) implies S < T. Axiom of Full Reflection for κ. Every stationary subset of κ reflects fully at regular cardinals.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2307/2374864">doi:10.2307/2374864</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kuxnm2ggmbfgtjpsiu3c4i4v3e">fatcat:kuxnm2ggmbfgtjpsiu3c4i4v3e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20050120001856/http://shelah.logic.at:80/files/383.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/e7/d5/e7d5f6bc251abe1e571ec49c66f3b150cb368016.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2307/2374864"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> jstor.org </button> </a>

Existence of almost free abelian groups and reflection of stationary set [article]

Saharon Shelah
<span title="1996-06-15">1996</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We answer a question of Foreman and Magidor on reflection of stationary subsets of S_< aleph_2(lambda) = a subseteq lambda : |a| < aleph_2]. section 3 - NPT is not transitive.  ...  The set S = {i < λ :< i >∈ S} is stationary (as S is a λ-set).  ...  One question of Foreman and Magidor asks for consistency of the following reflection principle: ( * ) λ if S ⊆ S <ℵ2 (λ) is a stationary set (of S <ℵ2 (λ), not of λ), each a ∈ S is ω-closed (i.e. cf(δ)  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/9606229v1">arXiv:math/9606229v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bjbhvslzhnbl3pcgqdupevhx6m">fatcat:bjbhvslzhnbl3pcgqdupevhx6m</a> </span>
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Dense non-reflection for stationary collections of countable sets

David Asperó, John Krueger, Yasuo Yoshinobu
<span title="">2009</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/bnojym2hjzcgnpa4wixi2axhnq" style="color: black;">Annals of Pure and Applied Logic</a> </i> &nbsp;
We prove that PFA is consistent with dense non-reflection in Pω 1 (λ), which means that every stationary subset of Pω 1 (λ) contains a stationary subset which does not reflect to any set of size ℵ 1 .  ...  We present several forcing posets for adding a non-reflecting stationary subset of Pω 1 (λ), where λ ≥ ω 2 .  ...  Fix a stationary set S ⊆ P ω 1 (λ). We will find a stationary set T ⊆ S which does not reflect to any set of size ℵ 1 .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.apal.2009.06.002">doi:10.1016/j.apal.2009.06.002</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ba5kcnnwprasnlgvyflpug7v6i">fatcat:ba5kcnnwprasnlgvyflpug7v6i</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170706092134/https://archive.uea.ac.uk/~bfe12ncu/dnrsccs.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/12/59/12597dce295293c623e5f88d2fa5b78ba814c3c2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.apal.2009.06.002"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

The failure of diamond on a reflecting stationary set

Moti Gitik, Assaf Rinot
<span title="2012-04-01">2012</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;
We establish the consistency of existence of a stationary subset of [ℵ ω+1 ] ω that cannot be thinned out to a stationary set on which the supfunction is injective.  ...  It is shown that the failure of ♦ S , for a set S ⊆ ℵ ω+1 that reflects stationarily often, is consistent with GCH and AP ℵ ω , relative to the existence of a supercompact cardinal.  ...  We now consider a third model, establishing that a very good scale has no effect on the validity of diamond for reflecting stationary sets. Theorem 1.11.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0002-9947-2011-05355-9">doi:10.1090/s0002-9947-2011-05355-9</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ec62wwxroradrg362h43g74c4u">fatcat:ec62wwxroradrg362h43g74c4u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190503035659/https://www.ams.org/journals/tran/2012-364-04/S0002-9947-2011-05355-9/S0002-9947-2011-05355-9.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/cc/00/cc005af1f59ce6f1155e74f89c1c67bc7868b5c4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0002-9947-2011-05355-9"> <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>

On reflection of stationary sets in $\mathcal {P}_\kappa \lambda $

Thomas Jech, Saharon Shelah
<span title="1999-04-20">1999</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;
It is consistent that the set E 1 is stationary and that every stationary subset of E 0 reflects at almost every a ∈ E 1 .  ...  A stationary set S ⊆ P κ λ reflects at a if the set S ∩ P κa a is a stationary set in P κa a. The question underlying our investigation is to what extent can stationary sets reflect.  ...  We are concerned with reflection of stationary sets. Reflection properties of stationary sets of ordinals have been extensively studied, starting with [7] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0002-9947-99-02448-4">doi:10.1090/s0002-9947-99-02448-4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ns5ayayy5jbmhlwu4365wdcz7e">fatcat:ns5ayayy5jbmhlwu4365wdcz7e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200812073236/https://www.ams.org/journals/tran/2000-352-06/S0002-9947-99-02448-4/S0002-9947-99-02448-4.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/ef/5b/ef5b10a7cc3937a96ea585a6a0e4c9955be45afa.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0002-9947-99-02448-4"> <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>

REFLECTION OF STATIONARY SETS AND THE TREE PROPERTY AT THE SUCCESSOR OF A SINGULAR CARDINAL

LAURA FONTANELLA, MENACHEM MAGIDOR
<span title="2017-01-23">2017</span> <i title="Cambridge University Press (CUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4l7nckgxmbcgvj5vxsioq6qwyq" style="color: black;">Journal of Symbolic Logic (JSL)</a> </i> &nbsp;
We show that from infinitely many supercompact cardinals one can force a model of ZFC where both the tree property and the stationary reflection hold at א ω 2+1.  ...  Stationary set reflection and the failure of the tree property at ℵ ω 2 +1 In this section we show that the stationary set reflection at ℵ ω 2 +1 does not imply the tree property.  ...  set reflection.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1017/jsl.2016.13">doi:10.1017/jsl.2016.13</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/omprbt6t2nce5johwj3oindtke">fatcat:omprbt6t2nce5johwj3oindtke</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190309101601/http://pdfs.semanticscholar.org/f7a9/45022018c19094da46723134b0807bebe3f8.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/f7/a9/f7a945022018c19094da46723134b0807bebe3f8.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1017/jsl.2016.13"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> cambridge.org </button> </a>

Derived topologies on ordinals and stationary reflection

Joan Bagaria
<span title="">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;
We characterize the non-isolated points in the ξ-th topology as those ordinals that satisfy a strong iterated form of stationary reflection, which we call ξ-simultaneous-reflection.  ...  We prove some properties of the ideals of non-ξ-simultaneous-stationary sets and identify their tight connection with indescribable cardinals.  ...  We begin with some definitions that generalize the notions of stationary set and stationary reflection. Definition 2.6.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/tran/7366">doi:10.1090/tran/7366</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fwezdsnnu5h5zj6vkldjd4ys3m">fatcat:fwezdsnnu5h5zj6vkldjd4ys3m</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180501050530/http://www.newton.ac.uk/files/preprints/ni16031.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/d5/c7/d5c7bc7c50ed5680fb2a08a0ac9d6a901d72d802.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/tran/7366"> <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>
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