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  1. Ultrafilters on Spaces of Partitions.James M. Henle & William S. Zwicker - 1982 - Journal of Symbolic Logic 47 (1):137-146.
  • On the Ultrafilters and Ultrapowers of Strong Partition Cardinals.J. M. Henle, E. M. Kleinberg & R. J. Watro - 1984 - Journal of Symbolic Logic 49 (4):1268-1272.
  • Ultrapowers Without the Axiom of Choice.Mitchell Spector - 1988 - Journal of Symbolic Logic 53 (4):1208-1219.
    A new method is presented for constructing models of set theory, using a technique of forming pseudo-ultrapowers. In the presence of the axiom of choice, the traditional ultrapower construction has proven to be extremely powerful in set theory and model theory; if the axiom of choice is not assumed, the fundamental theorem of ultrapowers may fail, causing the ultrapower to lose almost all of its utility. The pseudo-ultrapower is designed so that the fundamental theorem holds even if choice fails; this (...)
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  • Magidor-Like and Radin-Like Forcing.J. M. Henle - 1983 - Annals of Pure and Applied Logic 25 (1):59-72.
  • Calculus on Strong Partition Cardinals.James M. Henle - 2006 - Mathematical Logic Quarterly 52 (6):585-594.
    In [1] it was shown that if κ is a strong partition cardinal, then every function from [κ ]κ to [κ ]κ is continuous almost everywhere. In this investigation, we explore whether such functions are differentiable or integrable in any sense. Some of them are.
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  • Concerning Ultrafilters on Ultrapowers.J. M. Henle - 1987 - Journal of Symbolic Logic 52 (1):149-151.
  • Model Theory Under the Axiom of Determinateness.Mitchell Spector - 1985 - Journal of Symbolic Logic 50 (3):773-780.
    We initiate the study of model theory in the absence of the Axiom of Choice, using the Axiom of Determinateness as a powerful substitute. We first show that, in this context, L ω 1 ω is no more powerful than first-order logic. The emphasis then turns to upward Lowenhein-Skolem theorems; ℵ 1 is the Hanf number of first-order logic, of L ω 1 ω , and of a strong fragment of L ω 1 ω . The main technical innovation is (...)
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  • Weak Strong Partition Cardinals.J. M. Henle - 1984 - Journal of Symbolic Logic 49 (2):555-557.
  • Spector Forcing.J. M. Henle - 1984 - Journal of Symbolic Logic 49 (2):542-554.
    Forcing with [κ] κ over a model of set theory with a strong partition cardinal, M. Spector produced a generic ultrafilter G on κ such that κ κ /G is not well-founded. Theorem. Let G be Spector-generic over a model M of $ZF + DC + \kappa \rightarrow (\kappa)^\kappa_\alpha, \kappa > \omega$ , for all $\alpha . 1) Every cardinal (well-ordered or not) of M is a cardinal of M[ G]. 2) If A ∈ M[ G] is a well-ordered subset (...)
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