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Analytic ideals and cofinal types
1999
Annals of Pure and Applied Logic
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We also study 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? ...
doi:10.1016/s0168-0072(98)00065-7
fatcat:64v66i4wm5foxiupdym6xnjzua
Cofinal types of topological directed orders
2004
Annales de l'Institut Fourier
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We investigate the structure of the Tukey ordering among directed orders arising naturally in topology 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. ...
doi:10.5802/aif.2070
fatcat:pwlg5ruhkjbv3j267awzgpx3sq
Tukey Order, Calibres and the Rationals
[article]
2016
arXiv
pre-print
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Particular emphasis is placed on the position of K(M) when M is: completely metrizable, the rationals Q, co-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. ...
arXiv:1606.06493v2
fatcat:6ik5numlnrdq5bvx7baegeol6m
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
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Thus, all these statements are also consistent 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. ...
doi:10.1090/s0002-9947-1987-0876466-8
fatcat:ta6dzmf6ojh5zngewj2uvzndvy
Page 32 of Mathematical Reviews Vol. , Issue 93a
[page]
1993
Mathematical Reviews
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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. ...
Dimension zero vs measure zero
1999
Proceedings of the American Mathematical Society
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Similar questions concerning perfectly meager sets 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 . ...
doi:10.1090/s0002-9939-99-05225-9
fatcat:spufqea4mbh67lapuj5n5vehcy
On a σ-ideal of compact sets
2010
Topology and its Applications
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Soc. 137 (3) (2009) 1115-1125] a G δ σ -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 ]. ...
doi:10.1016/j.topol.2009.06.014
fatcat:s5gr24iejzbv7b6fnj2uzp6sr4
Page 3632 of Mathematical Reviews Vol. , Issue 89G
[page]
1989
Mathematical Reviews
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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 ¥;). ...
Maximal Tukey types, P-ideals and the weak Rudin-Keisler order
[article]
2019
arXiv
pre-print
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This discussion segues into an examination of a refinement of the Tukey order -- known as the "weak Rudin-Keisler order" -- 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. ...
arXiv:1902.00968v2
fatcat:siird2dzfje6dpxwnqkicycihq
Analytic gaps
1996
Fundamenta Mathematicae
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For every nonatomic 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. ...
doi:10.4064/fm-150-1-55-66
fatcat:eqlmkjb2evbinpgxspp6trr3h4
Page 3160 of Mathematical Reviews Vol. , Issue 90F
[page]
1990
Mathematical Reviews
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(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. ...
Cofinal families of Borel equivalence relations and quasiorders
2005
Journal of Symbolic Logic (JSL)
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There is an 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. ...
doi:10.2178/jsl/1129642127
fatcat:dlb4kye6ubaspkiqqeo2qqazky
Page 3994 of Mathematical Reviews Vol. , Issue 83j
[page]
1983
Mathematical Reviews
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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’. ...
Model Theory Methods for Topological Groups
2018
Bulletin of Symbolic Logic
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This correspondence can be inverted 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 ...
doi:10.1017/bsl.2018.32
fatcat:wgj65guzljh6xazhthsokheyv4
Page 1204 of Mathematical Reviews Vol. 34, Issue 5
[page]
1967
Mathematical Reviews
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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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