Monotone hulls for N ∩ M

Andrzej Rosłanowski; Saharon Shelah

doi:10.1007/s10998-014-0042-3

Monotone hulls for N ∩ M

Andrzej Rosłanowski, Saharon Shelah^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Using the method of decisive creatures [see Kellner and Shelah (J Symb Log 74:73–104, 2009)] we show the consistency of “there is no increasing (Formula presented.)–chain of Borel sets and (Formula presented.). Hence, consistently, there are no monotone Borel hulls for the ideal (Formula presented.). This answers Balcerzak and Filipczak (Math Log Q 57:186–193, 2011 [Questions 23, 24]). Next we use finite support iteration of ccc forcing notions to show that there may be monotone Borel hulls for the ideals (Formula presented.) even if they are not generated by towers.

Original language	English
Pages (from-to)	79-95
Number of pages	17
Journal	Periodica Mathematica Hungarica
Volume	69
Issue number	1
DOIs	https://doi.org/10.1007/s10998-014-0042-3
State	Published - 17 Oct 2014

Bibliographical note

Publisher Copyright:
© 2014, Akadémiai Kiadó, Budapest, Hungary.

Keywords

03E15
Primary 03E17
Secondary 03E35

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10.1007/s10998-014-0042-3

Cite this

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Monotone hulls for N ∩ M

Abstract

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Keywords

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