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Starting with infinitely many weakly compact cardinals, we show that the tree property at every even cardinal <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201600028-math-0004.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201600028:malq201600028-math-0004\"\/>, <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201600028-math-0005.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201600028:malq201600028-math-0005\"\/>, is consistent with an arbitrary continuum function below <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201600028-math-0006.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201600028:malq201600028-math-0006\"\/> which satisfies <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201600028-math-0007.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201600028:malq201600028-math-0007\"\/>, <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201600028-math-0008.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201600028:malq201600028-math-0008\"\/>. Next, starting with infinitely many Mahlo cardinals, we show that the weak tree property at every cardinal <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201600028-math-0009.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201600028:malq201600028-math-0009\"\/>, <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201600028-math-0010.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201600028:malq201600028-math-0010\"\/>, is consistent with an arbitrary continuum function below <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201600028-math-0011.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201600028:malq201600028-math-0011\"\/> which satisfies <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201600028-math-0012.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201600028:malq201600028-math-0012\"\/>, <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201600028-math-0013.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201600028:malq201600028-math-0013\"\/>. Thus the tree property has no provable effect on the continuum function below <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201600028-math-0014.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201600028:malq201600028-math-0014\"\/> except for the trivial requirement that the tree property at <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201600028-math-0015.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201600028:malq201600028-math-0015\"\/> implies <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201600028-math-0016.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201600028:malq201600028-math-0016\"\/> for every infinite \u03ba.<\/jats:p>","DOI":"10.1002\/malq.201600028","type":"journal-article","created":{"date-parts":[[2018,4,15]],"date-time":"2018-04-15T00:27:48Z","timestamp":1523752068000},"page":"89-102","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["The tree property and the continuum function below"],"prefix":"10.1002","volume":"64","author":[{"given":"Radek","family":"Honzik","sequence":"first","affiliation":[{"name":"Department of Logic Charles University Celetn\u00e1 20 Praha 1 116 42 Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"\u0160\u00e1rka","family":"Stejskalov\u00e1","sequence":"additional","affiliation":[{"name":"Department of Logic Charles University Celetn\u00e1 20 Praha 1 116 42 Czech 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