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Locally countable models of Σ1-separation

Published online by Cambridge University Press:  12 March 2014

Fred G. Abramson
Fred G. Abramson*
Affiliation:
University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201 Stanford University, Stanford, California 94305
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Abstract

Let α be any countable admissible ordinal greater than ω. There is a transitive set A such that A is admissible, locally countable, OnA = α, and A satisfies Σ1-separation. In fact, if B is any nonstandard model of KP + ∀x ⊆ ω (the hyperjump of x exists), the ordinal standard part of B is greater than ω, and every standard ordinal in B is countable in B, then HCB ∩ (standard part of B) satisfies Σ-separation.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 46 , Issue 1 , March 1981 , pp. 96 - 100
Copyright
Copyright © Association for Symbolic Logic 1981

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References

REFERENCES

[1]Abramson, F. G., Σ 1-separation, this Journal, vol. 44 (1979), pp. 374–382.Google Scholar
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[5]Vaught, R., Descriptive set theory in Lω1ω, Cambridge Summer School in Mathematical Logic, Lecture Notes in Mathematics, vol. 337, Springer, Berlin and New York, 1973, pp. 574–598.Google Scholar