Skip to main content
×
Home
    • Aa
    • Aa

The core model for sequences of measures. I

  • William J. Mitchell (a1)
Abstract

The model K() presented in this paper is a new inner model of ZFC which can contain measurable cardinals of high order. Like the model L() of [14], from which it is derived, K() is constructed from a sequence of filters such that K() satisfies for each (α, β) ε domain () that (α,β) is a measure of order β on α and the only measures in K() are the measures (α,β). Furthermore K(), like L(), has many of the basic properties of L: the GCH and ⃟ hold and there is a definable well ordering which is on the reals. The model K() is derived from L() by using techniques of Dodd and Jensen [2–5] to build in absoluteness for measurability and related properties.

Copyright
References
Hide All
[1] E. L. Bull Jr. Successive large cardinals. Ann. Math. Logic 15 (1978), 161191.

[3] A. J. Dodd and R. Jensen . The core model. Ann. Math. Logic 20 (1981), 4375.

[5] A. J. Dodd and R. Jensen . The covering lemma for L(U). Ann. Math. Logic 22 (1982), 127135.

[7] R. Jensen . The fine structure of the constructible hierarchy. Ann. Math. Logic 4 (1972), 229309.

[9] A. Kanamori and M. Magidor . The evolution of large cardinals in set theory. In Higher Set Theory, Lecture Notes in Math. vol. 699 (Springer-Verlag, 1978), 99275.

[10] K. Kunen . Some applications of iterated ultrapowers in set theory. Ann. Math. Logic 1 (1970), 179227.

[12] M. Magidor . On the singular cardinals problem, II. Ann. of Math. 106 (1977), 517547.

[18] R. M. Solovay , W. N. Reinhart and A. Kanamori . Strong axioms of infinity and elementary embeddings. Ann. Math. Logic 13 (1978), 73116.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 13 *
Loading metrics...

Abstract views

Total abstract views: 54 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 17th October 2017. This data will be updated every 24 hours.