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Applications of pcf for mild large cardinals to elementary embeddings [article]

Moti Gitik, Saharon Shelah
<span title="2013-07-23">2013</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
As an application we show that: if kappa is a measurable cardinal and j:V to M is the elementary embedding by a kappa-complete ultrafilter over kappa, then for every tau the following holds: 1. if j(tau  ...  The following pcf results are proved: 1. Assume that kappa > aleph_0 is a weakly compact cardinal. Let mu > 2^kappa be a singular cardinal of cofinality kappa.  ...  Applications. Let κ be a measurable cardinal, U be a κ-complete non-principle ultrafilter over κ and let j U : V → M ≃ κ V /U be the corresponding elementary embedding.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1307.5977v1">arXiv:1307.5977v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/giqyzvwejngazgdrytajqp2pki">fatcat:giqyzvwejngazgdrytajqp2pki</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200826161339/https://arxiv.org/pdf/1307.5977v1.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/e3/9c/e39cc73d5a42af03ff91a645f9f8de56393adf39.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1307.5977v1" 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>

Applications of pcf for mild large cardinals to elementary embeddings

Moti Gitik, Saharon Shelah
<span title="">2013</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;
As an application we show that: if κ is a measurable cardinal and j : V → M is the elementary embedding by a κcomplete ultrafilter over a measurable cardinal κ, then for every τ the following holds: 3.  ...  The following pcf results are proved: 1. Assume that κ > ℵ 0 is a weakly compact cardinal. Let µ > 2 κ be a singular cardinal of cofinality κ.  ...  Fremlin for cardinals of cofinality κ: 6 Corollary 3.6 Let W be a non-principal κ-complete ultrafilter on κ and j W : V → M W the corresponding elementary embedding.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.apal.2013.03.002">doi:10.1016/j.apal.2013.03.002</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bzmw3hmodjhcppvtbpxsk5lgda">fatcat:bzmw3hmodjhcppvtbpxsk5lgda</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20130409132128/http://www.math.tau.ac.il/~gitik/applemb.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/4c/8e/4c8ea03de1a512afedbfcd9cc6d74bddac0a43c6.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.apal.2013.03.002"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Singular Cardinals and the PCF Theory

Thomas Jech
<span title="">1995</span> <i title="Cambridge University Press (CUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nxnim3i24fhcvkvgruk2dej7yu" style="color: black;">Bulletin of Symbolic Logic</a> </i> &nbsp;
The work on the singular cardinals problem has led to many often surprising results, culminating in a beautiful theory of Saharon Shelah called the pcf theory ("pcf" stands for "possible cofinalities")  ...  Among the most remarkable discoveries in set theory in the last quarter century is the rich structure of the arithmetic of singular cardinals, and its deep relationship to large cardinals.  ...  One of the basic observations is that the existence of measurable cardinals is equivalent to the existence of a nontrivial elementary embedding j : V + A4 where M is some transitive model.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2307/421130">doi:10.2307/421130</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2e4jbjbaebbcrgljim4lzuk5oy">fatcat:2e4jbjbaebbcrgljim4lzuk5oy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20080221180643/http://www.math.psu.edu/jech/preprints/singular-publ.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/6f/ee/6fee2a273c3f4a90446e4a41e93accec8e28c202.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2307/421130"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> jstor.org </button> </a>

Forcing Axioms, Supercompact Cardinals, Singular Cardinal Combinatorics

Matteo Viale
<span title="">2008</span> <i title="Cambridge University Press (CUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nxnim3i24fhcvkvgruk2dej7yu" style="color: black;">Bulletin of Symbolic Logic</a> </i> &nbsp;
Also in this case the result can be translated in a large cardinal property, however this requires a familiarity with a rather large fragment of Shelah's pcf-theory.  ...  The purpose of this communication is to present some recent advances on the consequences that forcing axioms and large cardinals have on the combinatorics of singular cardinals.  ...  cardinal hypothesis) with different -sequences of ordinals and an elementary embedding between them.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2178/bsl/1208358846">doi:10.2178/bsl/1208358846</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dw2rmhz54reldbz3dlznzghv44">fatcat:dw2rmhz54reldbz3dlznzghv44</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20081031164522/http://www.logic.univie.ac.at/~matteo/BSLMV.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/9f/9c/9f9c75489d33b13a7906d1ca79a63f5de4c5cbbb.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2178/bsl/1208358846"> <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>

Analytical Guide and updates for "Cardinal Arithmetic" [article]

Saharon Shelah
<span title="2000-09-05">2000</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Part A: A revised version of the guide in "Cardinal Arithmetic" ([Sh:g]), with corrections and expanded to include later works. Part B: Corrections to [Sh:g].  ...  Part D: Contains a list of relevant references.  ...  pcf V {cf V (θ) : θ ∈ pcf V (a)} = {cf V (λ) : λ ∈ pcf W ({cf W (θ) : θ ∈ Application of ranks (see 2.2) to partition calculus: Shelah Stanley [ShSt 419].  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/9906022v2">arXiv:math/9906022v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wwrjhje7f5hpvh7djj2t2o7p6i">fatcat:wwrjhje7f5hpvh7djj2t2o7p6i</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-math9906022/math9906022.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/9906022v2" 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>

Non-existence of universals for classes like reduced torsion free abelian groups under embeddings which are not necessarily pure [chapter]

Saharon Shelah
<span title="2019-08-16">2019</span> <i title="CRC Press"> Advances in Algebra and Model Theory </i> &nbsp;
We say M ∈ K is universal for K if any member N of K of cardinality not bigger than the cardinality of M can be embedded into M . This is a natural, often raised, problem.  ...  We try to draw consequences of cardinal arithmetic to non-existence of universal members for such natural classes. Date: September 1995.  ...  Anyhow this is K tr λ i :i≤ω not K rs(p) λω , so we proceed to reduce this problem to the previous one under a mild variant of MA.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1201/9780367810603-15">doi:10.1201/9780367810603-15</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gvvpd5spafdqtoqfya77dc3mnq">fatcat:gvvpd5spafdqtoqfya77dc3mnq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20160407082816/http://shelah.logic.at/files/552.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/14/9d/149d5798ee76375fb357d0561ff8be34f8f2dbf9.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1201/9780367810603-15"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Non existence of universals for classes like reduced torsion free abelian groups under non neccessarily pure embeddings [article]

Saharon Shelah
<span title="1996-09-15">1996</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We try to draw consequences of cardinal arithmetic to non--existence of universal members for such natural classes.  ...  We say M in K is universal for K if any member N of K of cardinality not bigger than the cardinality of M can be embedded into M . This is a natural, often raised, problem.  ...  Anyhow this is K tr λi:i≤ω not K rs(p) λω , so we proceed to reduce this problem to the previous one under a mild variant of MA.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/9609217v1">arXiv:math/9609217v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/q3twiysgdraoxht52hpttjqrs4">fatcat:q3twiysgdraoxht52hpttjqrs4</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-math9609217/math9609217.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/9609217v1" 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>

Ultrafilters on singular cardinals of uncountable cofinality [article]

James Cummings, Charles Morgan
<span title="2019-07-26">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We prove that consistently there is a singular cardinal κ of uncountable cofinality such that 2^κ is weakly inaccessible, and every regular cardinal strictly between κ and 2^κ is the character of some  ...  A condition can be extended by performing a finite series of "elementary" extensions. One type of elementary extension is simply to shrink some A i .  ...  One type of elementary extension is to extend (f, A) to (f ′ , A ′ ) where f ′ ↾ dom(f ) = f and A ′ ↾ dom(f ) ⊆ A.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1907.11765v1">arXiv:1907.11765v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/oh6er34yrrad3k7ptzxyvphgn4">fatcat:oh6er34yrrad3k7ptzxyvphgn4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200907011913/https://arxiv.org/pdf/1907.11765v1.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/a3/7d/a37d90ab4fd4cf3bd6110dde7f391104ccc4ae12.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1907.11765v1" 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>

Canonical structure in the universe of set theory: part two

James Cummings, Matthew Foreman, Menachem Magidor
<span title="">2006</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 a number of consistency results complementary to the ZFC results from our paper [J. Cummings, M. Foreman, M.  ...  We also give an alternative proof for the consistency of the existence of stationarily many non-good points, show that diagonal Prikry forcing preserves certain stationary reflection properties, and study  ...  Let M be the transitive collapse of N, let M * be the collapse of N * , and let j : M −→ M * be the elementary embedding from M to M * corresponding to the inclusion map from N to N * .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.apal.2005.11.007">doi:10.1016/j.apal.2005.11.007</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wjaikpyqjrhk3lgfgobfck5axq">fatcat:wjaikpyqjrhk3lgfgobfck5axq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190317014003/https://core.ac.uk/download/pdf/81996980.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/54/f0/54f0c4ece916c20fc77b72e1b4be09b43045ef82.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.apal.2005.11.007"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Canonical structure in the universe of set theory: part one

James Cummings, Matthew Foreman, Menachem Magidor
<span title="">2004</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 a number of consistency results complementary to the ZFC results from our paper [4] .  ...  We also give an alternative proof for the consistency of the existence of stationarily many non-good points, show that diagonal Prikry forcing preserves certain stationary reflection properties, and study  ...  It is routine to check that M * = U lt(M, U ) and j is the associated elementary embedding j M U . j has critical point equal to the collapse of κ n , so in particular j fixes the collapse of κ n−1 .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.apal.2004.04.002">doi:10.1016/j.apal.2004.04.002</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/f4ijyne4hjeldkfvp7shkccv6m">fatcat:f4ijyne4hjeldkfvp7shkccv6m</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20060910042852/http://www.math.cmu.edu/users/jcumming/papers/cfm2b.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/c6/d0/c6d07aeefe456fc7f5a55fee8dcecefc153f6437.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.apal.2004.04.002"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Some consequences of reflection on the approachability ideal

Assaf Sharon, Matteo Viale
<span title="2010-03-08">2010</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 study the approachability ideal I[κ + ] in the context of large cardinals and properties of the regular cardinals below a singular κ.  ...  We also apply our result to show that the Chang conjecture (κ + , κ) (ℵ 2 , ℵ 1 ) fails in models of MM for all singular cardinals κ.  ...  Let j : V → M be the associated generic elementary embedding. Since I is λ-complete and fine, we have that the critical point of j is λ.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0002-9947-10-04976-7">doi:10.1090/s0002-9947-10-04976-7</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7hc3c5qs3zc6jltuqmwwjdzzyi">fatcat:7hc3c5qs3zc6jltuqmwwjdzzyi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190430211945/https://www.ams.org/journals/tran/2010-362-08/S0002-9947-10-04976-7/S0002-9947-10-04976-7.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/00/f5/00f53751f485159341e2dd602e5a06c4d6c268c2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0002-9947-10-04976-7"> <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>

Good and bad points in scales

Chris Lambie-Hanson
<span title="2014-07-10">2014</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3egevcnserbbni4tcigsztdici" style="color: black;">Archive for Mathematical Logic</a> </i> &nbsp;
Finally, we investigate the ideal of subsets of singular cardinals of countable cofinality carrying good scales.  ...  We first analyze the PCF-theoretic structure of the Gitik-Sharon model, determining the extent of good and bad scales.  ...  So, in V [G], let A n | n < ω be such that, for all n < ω, A n ∈ I gd [κ]. We can assume that none of the A n 's is finite.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00153-014-0387-6">doi:10.1007/s00153-014-0387-6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ba2csq7usbcbdomjxsivms22by">fatcat:ba2csq7usbcbdomjxsivms22by</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20151214030649/http://math.huji.ac.il/~clambiehanson/scales.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/e2/91/e29104fb30b4a96efcbc93a6ee2134f52ab32dd8.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00153-014-0387-6"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Large cardinals and gap-1 morasses

Andrew D. Brooke-Taylor, Sy-David Friedman
<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;
This all contributes to the second author's outer model programme, the aim of which is to show that L-like principles can hold in outer models which nevertheless contain large cardinals.  ...  We present a new partial order for directly forcing morasses to exist that enjoys a significant homogeneity property.  ...  When we force morasses to exist in the presence of multiple large cardinals, it will be convenient for the sake of preservation of the large cardinal property to use a partial order which lends itself  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.apal.2008.10.007">doi:10.1016/j.apal.2008.10.007</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qvhakyso3ze3blnw6tbufyqe64">fatcat:qvhakyso3ze3blnw6tbufyqe64</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20110401112437/http://www.maths.bristol.ac.uk/~maadbt/lcg1m.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/7b/77/7b77f1aa16afe944edab0c2cdc3e570a29076600.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.apal.2008.10.007"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Embeddings of Cohen Algebras

Saharon Shelah, Jindřich Zapletal
<span title="">1997</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/37jjomjmvfhrzf3di2gjnrrfuu" style="color: black;">Advances in Mathematics</a> </i> &nbsp;
So we choose a large regular cardinal * and a countable elementary submodel M O H * such that Q, P, p, (q 0 , m 0 ) are all in M.  ...  The heart of the matter lies in introducing a regular embedding of C(+ 1 ) to a given algebra B of uniform density + 1 by a sufficiently mild forcing.  ... 
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Embeddings of Cohen algebras [article]

Saharon Shelah, Jindřich Zapletal
<span title="1995-02-15">1995</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
regular open sets in the space 0,1^kappa, for kappa an infinite cardinal.  ...  C(kappa) is much easier to analyse than B(kappa) : C(kappa) has a dense subset of size kappa, while the density of B(kappa) depends on the cardinal characteristics of the real line; and the definition  ...  So we choose a large regular cardinal λ and a countable elementary submodel M ≺ H λ such that Q, P, p, q 0 , m 0 are all in M.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/9502230v1">arXiv:math/9502230v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nhysn7h6hnfxjlrnucjjtbmrlm">fatcat:nhysn7h6hnfxjlrnucjjtbmrlm</a> </span>
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