The tree property and the continuum function below
We say that a regular cardinal κ, , has the tree property if there are no κ‐Aronszajn trees; we say that κ has the weak tree property if there are no special κ‐Aronszajn trees. Starting with infinitely many weakly compact cardinals, we show that the tree property at every even cardinal , , is consis...
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| Veröffentlicht in: | Mathematical logic quarterly 2018-04, Vol.64 (1-2), p.89-102 |
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| container_end_page | 102 |
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| container_issue | 1-2 |
| container_start_page | 89 |
| container_title | Mathematical logic quarterly |
| container_volume | 64 |
| creator | Honzik, Radek Stejskalová, Šárka |
| description | We say that a regular cardinal κ,
, has the tree property if there are no κ‐Aronszajn trees; we say that κ has the weak tree property if there are no special κ‐Aronszajn trees. Starting with infinitely many weakly compact cardinals, we show that the tree property at every even cardinal
,
, is consistent with an arbitrary continuum function below
which satisfies
,
. Next, starting with infinitely many Mahlo cardinals, we show that the weak tree property at every cardinal
,
, is consistent with an arbitrary continuum function below
which satisfies
,
. Thus the tree property has no provable effect on the continuum function below
except for the trivial requirement that the tree property at
implies
for every infinite κ. |
| doi_str_mv | 10.1002/malq.201600028 |
| format | Article |
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, has the tree property if there are no κ‐Aronszajn trees; we say that κ has the weak tree property if there are no special κ‐Aronszajn trees. Starting with infinitely many weakly compact cardinals, we show that the tree property at every even cardinal
,
, is consistent with an arbitrary continuum function below
which satisfies
,
. Next, starting with infinitely many Mahlo cardinals, we show that the weak tree property at every cardinal
,
, is consistent with an arbitrary continuum function below
which satisfies
,
. Thus the tree property has no provable effect on the continuum function below
except for the trivial requirement that the tree property at
implies
for every infinite κ.</description><identifier>ISSN: 0942-5616</identifier><identifier>EISSN: 1521-3870</identifier><identifier>DOI: 10.1002/malq.201600028</identifier><language>eng</language><ispartof>Mathematical logic quarterly, 2018-04, Vol.64 (1-2), p.89-102</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c848-d1d73fbd5000c4a36b4f95157ede8dc27bd7c33af16d8c7bebb40017e8aeb9a33</citedby><cites>FETCH-LOGICAL-c848-d1d73fbd5000c4a36b4f95157ede8dc27bd7c33af16d8c7bebb40017e8aeb9a33</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Honzik, Radek</creatorcontrib><creatorcontrib>Stejskalová, Šárka</creatorcontrib><title>The tree property and the continuum function below</title><title>Mathematical logic quarterly</title><description>We say that a regular cardinal κ,
, has the tree property if there are no κ‐Aronszajn trees; we say that κ has the weak tree property if there are no special κ‐Aronszajn trees. Starting with infinitely many weakly compact cardinals, we show that the tree property at every even cardinal
,
, is consistent with an arbitrary continuum function below
which satisfies
,
. Next, starting with infinitely many Mahlo cardinals, we show that the weak tree property at every cardinal
,
, is consistent with an arbitrary continuum function below
which satisfies
,
. Thus the tree property has no provable effect on the continuum function below
except for the trivial requirement that the tree property at
implies
for every infinite κ.</description><issn>0942-5616</issn><issn>1521-3870</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNo9j0tLxDAUhYMoOI5uXecPtN6bNE26lMEXDLjpvuRxg5W-TFtk_r0dFFeHczicw8fYPUKOAOKht91XLgBL2Jy5YDtUAjNpNFyyHVSFyFSJ5TW7mefPraJQw46J-oP4koj4lMaJ0nLidgh82VI_Dks7rGvP4zr4pR0H7qgbv2_ZVbTdTHd_umf181N9eM2O7y9vh8dj5k1hsoBBy-iC2q58YWXpilgpVJoCmeCFdkF7KW3EMhivHTlXAKAmY8lVVso9y39nfRrnOVFsptT2Np0ahOYM3JyBm39g-QOKJ0oV</recordid><startdate>201804</startdate><enddate>201804</enddate><creator>Honzik, Radek</creator><creator>Stejskalová, Šárka</creator><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>201804</creationdate><title>The tree property and the continuum function below</title><author>Honzik, Radek ; Stejskalová, Šárka</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c848-d1d73fbd5000c4a36b4f95157ede8dc27bd7c33af16d8c7bebb40017e8aeb9a33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Honzik, Radek</creatorcontrib><creatorcontrib>Stejskalová, Šárka</creatorcontrib><collection>CrossRef</collection><jtitle>Mathematical logic quarterly</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Honzik, Radek</au><au>Stejskalová, Šárka</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The tree property and the continuum function below</atitle><jtitle>Mathematical logic quarterly</jtitle><date>2018-04</date><risdate>2018</risdate><volume>64</volume><issue>1-2</issue><spage>89</spage><epage>102</epage><pages>89-102</pages><issn>0942-5616</issn><eissn>1521-3870</eissn><abstract>We say that a regular cardinal κ,
, has the tree property if there are no κ‐Aronszajn trees; we say that κ has the weak tree property if there are no special κ‐Aronszajn trees. Starting with infinitely many weakly compact cardinals, we show that the tree property at every even cardinal
,
, is consistent with an arbitrary continuum function below
which satisfies
,
. Next, starting with infinitely many Mahlo cardinals, we show that the weak tree property at every cardinal
,
, is consistent with an arbitrary continuum function below
which satisfies
,
. Thus the tree property has no provable effect on the continuum function below
except for the trivial requirement that the tree property at
implies
for every infinite κ.</abstract><doi>10.1002/malq.201600028</doi><tpages>14</tpages></addata></record> |
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| ispartof | Mathematical logic quarterly, 2018-04, Vol.64 (1-2), p.89-102 |
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| language | eng |
| recordid | cdi_crossref_primary_10_1002_malq_201600028 |
| source | Access via Wiley Online Library |
| title | The tree property and the continuum function below |
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