Coherent Sequences

Todorčević, Stevo

doi:10.1007/978-1-4020-5764-9_4

Cited by 17 publications

(6 citation statements)

References 55 publications

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“…These results do not contradict the existence of Hausdorff gaps, see e.g. Definition 2.26 of [44]. This is because to obtain treetops and the transfer of the peculiar cut below, we restrict ourselves to some infinite subset of ω.…”

Section: Considered As a Functionmentioning

confidence: 79%

Cofinality spectrum theorems in model theory, set theory, and general topology

Malliaris

Shelah

2015

J. Amer. Math. Soc.

152

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We connect and solve two long-standing open problems in quite different areas: the model-theoretic question of whether S O P 2 SOP_2 is maximal in Keisler’s order, and the question from general topology/set theory of whether p = t \mathfrak {p} = \mathfrak {t} , the oldest problem on cardinal invariants of the continuum. We do so by showing these problems can be translated into instances of a more fundamental problem which we state and solve completely, using model-theoretic methods.

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Section: Considered As a Functionmentioning

confidence: 79%

Cofinality spectrum theorems in model theory, set theory, and general topology

Malliaris

Shelah

2015

J. Amer. Math. Soc.

152

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“…at each p > a, and applying Theorems 6.2 and 6.3. H By contrast, results of Todorcevic [22] give the following (see also [20]). We note that the second of these has recently been improved by Moore [15].…”

Section: Condition (1) Here Ensures That Letting a A = J + {B) P A mentioning

confidence: 94%

The nonstationary ideal in the ℙ_max extension

Larson

2007

J. symb. log.

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The forcing construction ℙmax, invented by W. Hugh Woodin, produces a model whose collection of subsets of ω1 is in some sense maximal. In this paper we study the Boolean algebra induced by the nonstationary ideal on ω1 in this model. Among other things we show that the induced quotient does not have a simply definable form. We also prove several results about saturation properties of the ideal in this extension.

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“…In the case where κ = 1, a ( , κ)-sequence is of course taken to be a sequence of club sets, rather than a sequence of singletons of club sets. This case has been studied extensively by Todorčević, see [27] for an overview. It is easy to see that if is a cardinal, then a ,κ sequence is also a ( + , κ) sequence.…”

Section: It Consists Of Countable Initial Segments Of Such a Functionmentioning

confidence: 99%

Hierarchies of (Virtual) Resurrection Axioms

Fuchs¹

2018

J. symb. log.

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I analyze the hierarchies of the bounded resurrection axioms and their “virtual” versions, the virtual bounded resurrection axioms, for several classes of forcings (the emphasis being on the subcomplete forcings). I analyze these axioms in terms of implications and consistency strengths. For the virtual hierarchies, I provide level-by-level equiconsistencies with an appropriate hierarchy of virtual partially super-extendible cardinals. I show that the boldface resurrection axioms for subcomplete or countably closed forcing imply the failure of Todorčević’s square at the appropriate level. I also establish connections between these hierarchies and the hierarchies of bounded and weak bounded forcing axioms.

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Coherent Sequences

Cited by 17 publications

References 55 publications

Cofinality spectrum theorems in model theory, set theory, and general topology

Cofinality spectrum theorems in model theory, set theory, and general topology

The nonstationary ideal in the ℙ_max extension

Hierarchies of (Virtual) Resurrection Axioms

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Coherent Sequences

Cited by 17 publications

References 55 publications

Cofinality spectrum theorems in model theory, set theory, and general topology

Cofinality spectrum theorems in model theory, set theory, and general topology

The nonstationary ideal in the ℙmax extension

Hierarchies of (Virtual) Resurrection Axioms

Contact Info

Product

Resources

About

The nonstationary ideal in the ℙ_max extension