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## Filters

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Analytic ideals and cofinal types

1999
*
Annals of Pure and Applied Logic
*

We also study

doi:10.1016/s0168-0072(98)00065-7
fatcat:64v66i4wm5foxiupdym6xnjzua
*ideals*associated to classical Banach spaces*and**ideals*of compacts sets in a Polish space. ... We study the class of*analytic**ideals*on the set of natural numbers ordered under Tukey reducibility. ... Is .F the maximum*cofinal**type*among*analytic*a-*ideals*of compact sets? ...##
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Cofinal types of topological directed orders

2004
*
Annales de l'Institut Fourier
*

We investigate the structure of the Tukey ordering among directed orders arising naturally in topology

doi:10.5802/aif.2070
fatcat:pwlg5ruhkjbv3j267awzgpx3sq
*and*measure theory. ... The relation D ≡ T E is equivalent to the existence of a directed partial order into which both D*and*E embed as*cofinal*subsets. We say then that D*and*E realize the same*cofinal**type*[14] . ... We establish a result about definability of*cofinal*subsets of*analytic**ideals*. ...##
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Tukey Order, Calibres and the Rationals
[article]

2016
*
arXiv
*
pre-print

Particular emphasis is placed on the position of K(M) when M is: completely metrizable, the rationals Q, co-

arXiv:1606.06493v2
fatcat:6ik5numlnrdq5bvx7baegeol6m
*analytic*or*analytic*. ... One partially ordered set, Q, is a Tukey quotient of another, P, denoted P ≥_T Q, if there is a map ϕ : P → Q carrying*cofinal*sets of P to*cofinal*sets of Q. ... Note also that the Tukey*type**and**cofinality*of a K(B) where B is totally imperfect*and*has size ≥ ℵ ω is dependent on what happens at ℵ ω . 3.3. General Calibres. ...##
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Near coherence of filters. II. Applications to operator ideals, the Stone-Čech remainder of a half-line, order ideals of sequences, and slenderness of groups

1987
*
Transactions of the American Mathematical Society
*

Thus, all these statements are also consistent

doi:10.1090/s0002-9947-1987-0876466-8
fatcat:ta6dzmf6ojh5zngewj2uvzndvy
*and*independent. ... We show that NCF is equivalent to the following statements, among others: (1) The*ideal*of compact operators on Hilbert space is not the sum of two smaller*ideals*. (2) The Stone-Cech remainder of a half-line ... Thus, a growth*type*is an*ideal*in w ~ w that is closed under doubling. Of the*ideals*discussed in the last section, B*and*w ~ w are growth*types*. ...##
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Page 32 of Mathematical Reviews Vol. , Issue 93a
[page]

1993
*
Mathematical Reviews
*

In the paper under review, the authors show that in the Cohen model for 2%° = N>, the property S — (

*cofinal*subset)3 (*and*also S — (*cofinal*subset);, for r,k € w) holds if*and*only if S has finite character ... (J-NAGOS) Mansfield*and*Solovay*type*results on covering plane sets by lines. Nagoya Math. J. 124 (1991), 145-155. Let 2 be a family of subsets of the plane R?*and*let x be a cardinal number. ...##
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Dimension zero vs measure zero

1999
*
Proceedings of the American Mathematical Society
*

Similar questions concerning perfectly meager sets

doi:10.1090/s0002-9939-99-05225-9
fatcat:spufqea4mbh67lapuj5n5vehcy
*and*other*types*of small sets are also discussed. ... It is shown that in a model of set theory it is so for separable metric spaces*and*that under the Martin's Axiom there are separable metric spaces of positive dimension yet of universal measure zero. ... If X is a space*and*J an*ideal*on X, call J proper if it contains all singletons*and*X / ∈ J . ...##
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On a σ-ideal of compact sets

2010
*
Topology and its Applications
*

Soc. 137 (3) (2009) 1115-1125] a G δ σ -

doi:10.1016/j.topol.2009.06.014
fatcat:s5gr24iejzbv7b6fnj2uzp6sr4
*ideal*of compact subsets of 2 ω*and*prove that it is not Tukey reducible to the*ideal*I 1/n = {H ⊆ ω: h∈H 1/h < ∞}. This result answers a question of S. ... Solecki*and*S. Todorčević in the negative. ... Thus*analytic*P -*ideals*are rich in*cofinal**types*. -We will show M ∩ K(2 ω ) < T I in Section 3. This gives a negative answer to [8, Question 3, p. 194 ]. ...##
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Page 3632 of Mathematical Reviews Vol. , Issue 89G
[page]

1989
*
Mathematical Reviews
*

A class of

*types*, called low*types*, is identified. These are the*types*which can be realized by a random element of some ultrapower. ... One concern is the*cofinality*of the Z-prod /*and*the coinitiality of the nonstandard part. These cardinals are called the*cofinality**and*coinitiality of 2. (CH implies these cardinals must be ¥;). ...##
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Maximal Tukey types, P-ideals and the weak Rudin-Keisler order
[article]

2019
*
arXiv
*
pre-print

This discussion segues into an examination of a refinement of the Tukey order -- known as the "weak Rudin-Keisler order" --

arXiv:1902.00968v2
fatcat:siird2dzfje6dpxwnqkicycihq
*and*its structure when restricted to these*ideals*of maximal Tukey*type*. ... Mirroring a result of Fremlin on the Tukey order, we also show that there is an*analytic*P-*ideal*above all other*analytic*P-*ideals*in the weak Rudin-Keisler. ... Two partial orders have the same Tukey*type*(or*cofinal**type*) iff each is Tukey-reducible to the other. Tukey himself examined*cofinal**types*in the context of convergence in topological spaces. ...##
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Analytic gaps

1996
*
Fundamenta Mathematicae
*

For every nonatomic

doi:10.4064/fm-150-1-55-66
fatcat:eqlmkjb2evbinpgxspp6trr3h4
*analytic*P-*ideal*A on N there is a Borel monotonic map from A onto a*cofinal*subset of NN . P r o o f. ... Suppose A is an*analytic**ideal*whose orthogonal A⊥ is not a P -*ideal*. Then there is a Borel monotonic map which transfers A to a*cofinal*subset of NN . P r o o f. ...##
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Page 3160 of Mathematical Reviews Vol. , Issue 90F
[page]

1990
*
Mathematical Reviews
*

(e) cf(Ky) > Ky.
03 MATHEMATICAL LOGIC

*AND*FOUNDATIONS 3160 Let Y*and*# denote the*ideal*of null sets*and*the*ideal*of meager sets, respectively. ... Silver proved that every*analytic*set is Ramsey, while A. Kechris showed that every*analytic*set is K,-regular. ...##
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Cofinal families of Borel equivalence relations and quasiorders

2005
*
Journal of Symbolic Logic (JSL)
*

There is an

doi:10.2178/jsl/1129642127
fatcat:dlb4kye6ubaspkiqqeo2qqazky
*analytic**ideal*on ω generating a complete*analytic*equivalence relation*and*any Borel equivalence relation reduces to one generated by a Borel*ideal*. ... Families of Borel equivalence relations*and*quasiorders that are*cofinal*with respect to the Borel reducibility ordering. ≤ B , are constructed. ... We construct an*analytic**ideal*I max generating a complete*analytic*equivalence relation. ...##
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Page 3994 of Mathematical Reviews Vol. , Issue 83j
[page]

1983
*
Mathematical Reviews
*

3:03.054 thesis [“Model theory of fields (decidability

*and*bounds for polynomial*ideals*)”, see Chapter III, Ph.D. Thesis, Rijksuniv. Utrecht, Utrecht, 1978]. ... From this it follows that for the least a of*cofinality*w, such that R, is KM-expandable there is exactly one expansion of R, to a model of KM + ‘all classes are ramified*analytical*’. ...##
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Model Theory Methods for Topological Groups

2018
*
Bulletin of Symbolic Logic
*

This correspondence can be inverted

doi:10.1017/bsl.2018.32
fatcat:wgj65guzljh6xazhthsokheyv4
*and*we extend it to*types**and*saturation. ... the second is the existence of a precipitous*ideal*on 1 . ... The first key result has applications on forcing projective or J 1+ (R) well-orderings of the reals, depending on the order*type*of the strong cardinals of K below V 1 ,*and*on 2-step stationary forcing ...##
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Page 1204 of Mathematical Reviews Vol. 34, Issue 5
[page]

1967
*
Mathematical Reviews
*

set of integers is

*cofinal*,*and*(iii) if na20, where n is a positive integer, then az0. ... A partition # of X into closed subsets is regenerate if feO(X), f|\K ¢ A\|K for all K ¢ X imply fe A,*and*if for every maximal*ideal*J of A there exists a unique K ¢ # such that (/|K)~ is a maximal*ideal*...
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