The strong reflecting property and Harrington's Principle

Preprint English OPEN
Cheng, Yong;
(2015)
  • Subject: Mathematics - Logic
    arxiv: Mathematics::General Topology | Astrophysics::Earth and Planetary Astrophysics | Mathematics::Logic

In this paper we characterize the strong reflecting property for $L$-cardinals for all $\omega_n$, characterize Harrington's Principle $HP(L)$ and its generalization and discuss the relationship between the strong reflecting property for $L$-cardinals and Harrington's P... View more
  • References (21)
    21 references, page 1 of 3

    13Note that the proof of [8, Theorem 18.20], as opposed to the proof of Theorem 3.3 above, is

    not done in Z4.

    14Examples of large cardinal notions compatible with L: inaccessible cardinal,reflecting car-

    nal, ineffable cardinal, 1-iterable cardinal, remarkable cardinal, 2-iterable cardinal and ω-Erdo¨s

    cardinal. [1] Yong Cheng, Forcing a set model of Z3 + Harrington's Principle, To appear in Mathematical

    Logic Quarterly. [2] Yong Cheng and Ralf Schindler, Harrington's Principle in higher order arithmetic, To appear

    in The Journal of Symbolic Logic. [3] James Cummings, Iterated Forcing and Elementary Embeddings, Chapter 12 in Handbook of

    Set Theory, Edited by Matthew Foreman and Akihiro Kanamori, Springer, Berlin, 2010. [4] Keith J.Devlin, Constructibility, Springer, Berlin, 1984. [5] Sy D. Friedman, Constructibility and Class Forcing, Chapter 8 in Handbook of Set Theory,

    Edited by Matthew Foreman and Akihiro Kanamori, Springer, Berlin, 2010. [6] Victoria Gitman, Joel David Hamkins, Thomas A. Johnstone, What is the theory ZF C

    without Powerset? See http://arxiv.org/abs/1110.2430 [7] L.A. Harrington, Analytic determinacy and 0♯, The Journal of Symbolic Logic, 43(1978),

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