13 found
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  1.  40
    Cofinal types of ultrafilters.Dilip Raghavan & Stevo Todorcevic - 2012 - Annals of Pure and Applied Logic 163 (3):185-199.
  2.  35
    Bounding, splitting, and almost disjointness.Jörg Brendle & Dilip Raghavan - 2014 - Annals of Pure and Applied Logic 165 (2):631-651.
    We investigate some aspects of bounding, splitting, and almost disjointness. In particular, we investigate the relationship between the bounding number, the closed almost disjointness number, the splitting number, and the existence of certain kinds of splitting families.
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  3.  17
    A long chain of P-points.Borisa Kuzeljevic & Dilip Raghavan - 2018 - Journal of Mathematical Logic 18 (1):1850004.
    The notion of a [Formula: see text]-generic sequence of P-points is introduced in this paper. It is proved assuming the Continuum Hypothesis that for each [Formula: see text], any [Formula: see text]-generic sequence of P-points can be extended to an [Formula: see text]-generic sequence. This shows that the CH implies that there is a chain of P-points of length [Formula: see text] with respect to both Rudin–Keisler and Tukey reducibility. These results answer an old question of Andreas Blass.
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  4.  12
    A small ultrafilter number at smaller cardinals.Dilip Raghavan & Saharon Shelah - 2020 - Archive for Mathematical Logic 59 (3-4):325-334.
    It is proved to be consistent relative to a measurable cardinal that there is a uniform ultrafilter on the real numbers which is generated by fewer than the maximum possible number of sets. It is also shown to be consistent relative to a supercompact cardinal that there is a uniform ultrafilter on \ which is generated by fewer than \ sets.
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  5.  38
    The Next Best Thing to a P-Point.Andreas Blass, Natasha Dobrinen & Dilip Raghavan - 2015 - Journal of Symbolic Logic 80 (3):866-900.
    We study ultrafilters onω2produced by forcing with the quotient of${\cal P}$(ω2) by the Fubini square of the Fréchet filter onω. We show that such an ultrafilter is a weak P-point but not a P-point and that the only nonprincipal ultrafilters strictly below it in the Rudin–Keisler order are a single isomorphism class of selective ultrafilters. We further show that it enjoys the strongest square-bracket partition relations that are possible for a non-P-point. We show that it is not basically generated but (...)
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  6.  16
    Separating families and order dimension of Turing degrees.Ashutosh Kumar & Dilip Raghavan - 2021 - Annals of Pure and Applied Logic 172 (5):102911.
  7.  22
    The density zero ideal and the splitting number.Dilip Raghavan - 2020 - Annals of Pure and Applied Logic 171 (7):102807.
    The main result of this paper is an improvement of the upper bound on the cardinal invariant $cov^*(L_0)$ that was discovered in [11]. Here $L_0$ is the ideal of subsets of the set of natural numbers that have asymptotic density zero. This improved upper bound is also dualized to get a better lower bound on the cardinal $non^*(L_0)$. En route some variations on the splitting number are introduced and several relationships between these variants are proved.
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  8.  8
    Lower Bounds of Sets of P-points.Borisa Kuzeljevic, Dilip Raghavan & Jonathan L. Verner - 2023 - Notre Dame Journal of Formal Logic 64 (3):317-327.
    We show that MAκ implies that each collection of Pc-points of size at most κ which has a Pc-point as an RK upper bound also has a Pc-point as an RK lower bound.
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  9.  10
    Complexity of Index Sets of Descriptive Set-Theoretic Notions.Reese Johnston & Dilip Raghavan - 2022 - Journal of Symbolic Logic 87 (3):894-911.
    Descriptive set theory and computability theory are closely-related fields of logic; both are oriented around a notion of descriptive complexity. However, the two fields typically consider objects of very different sizes; computability theory is principally concerned with subsets of the naturals, while descriptive set theory is interested primarily in subsets of the reals. In this paper, we apply a generalization of computability theory, admissible recursion theory, to consider the relative complexity of notions that are of interest in descriptive set theory. (...)
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  10.  48
    Gregory trees, the continuum, and Martin's axiom.Kenneth Kunen & Dilip Raghavan - 2009 - Journal of Symbolic Logic 74 (2):712-720.
    We continue the investigation of Gregory trees and the Cantor Tree Property carried out by Hart and Kunen. We produce models of MA with the Continuum arbitrarily large in which there are Gregory trees, and in which there are no Gregory trees.
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  11.  50
    Almost disjoint families and diagonalizations of length continuum.Dilip Raghavan - 2010 - Bulletin of Symbolic Logic 16 (2):240 - 260.
    We present a survey of some results and problems concerning constructions which require a diagonalization of length continuum to be carried out, particularly constructions of almost disjoint families of various sorts. We emphasize the role of cardinal invariants of the continuum and their combinatorial characterizations in such constructions.
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  12.  85
    P-ideal dichotomy and weak squares.Dilip Raghavan - 2013 - Journal of Symbolic Logic 78 (1):157-167.
    We answer a question of Cummings and Magidor by proving that the P-ideal dichotomy of Todorčević refutes ${\square}_{\kappa, \omega}$ for any uncountable $\kappa$. We also show that the P-ideal dichotomy implies the failure of ${\square}_{\kappa, < \mathfrak{b}}$ provided that $cf(\kappa) > {\omega}_{1}$.
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  13.  30
    2010 north american annual meeting of the association for symbolic logic.Alexander Razborov, Bob Coecke, Zoé Chatzidakis, Bjørn Kjos, Nicolaas P. Landsman, Lawrence S. Moss, Dilip Raghavan, Tom Scanlon, Ernest Schimmerling & Henry Towsner - 2011 - Bulletin of Symbolic Logic 17 (1):127-154.