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5Studies in the structure of some ancient scripts IV and VBulletin of the John Rylands Library 48 (1): 56-80. 1965.
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45A Flipping Characterization of Ramsey CardinalsZeitschrift fur mathematische Logik und Grundlagen der Mathematik 24 (1-6): 31-36. 1978.
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27The normal depth of filters on an infinite cardinalZeitschrift fur mathematische Logik und Grundlagen der Mathematik 36 (4): 293-296. 1990.
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11A Flipping Characterization of Ramsey CardinalsMathematical Logic Quarterly 24 (1‐6): 31-36. 1978.
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25The consistency of one fixed omegaJournal of Symbolic Logic 60 (1): 172-177. 1995.The paper "Partitions of Products" [DiPH] investigated the polarized partition relation $\begin{pmatrix}\omega\\\omega\\\omega\\\vdots\end{pmatrix} \rightarrow \begin{pmatrix}\alpha_1\\\alpha_1\\\alpha_2\\\vdots \end{pmatrix}$ The relation is consistent relative to an inaccessible cardinal if every α i is finite, but inconsistent if two are infinite. We show here that it consistent (relative to an inaccessible) for one to be infinite. Along the way, we prove an interesting proposition from ZFC c…Read more
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66Some consequences of an infinite-exponent partition relationJournal of Symbolic Logic 42 (4): 523-526. 1977.
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29Spector forcingJournal of Symbolic Logic 49 (2): 542-554. 1984.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 of M, then A ∈ M. Let Φ = κ κ /G. 3) There is an ultrafilter U on Φ such that ev…Read more
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28Second-order non-nonstandard analysisStudia Logica 74 (3). 2003.Following [3], we build higher-order models of analysis resembling the frameworks of nonstandard analysis. The models are entirely canonical, constructed without Choice. Weak transfer principles are developed and the models are applied to topology, graph theory, and measure theory. A Loeb-like measure is constructed.
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29Partition properties and Prikry forcing on simple spacesJournal of Symbolic Logic 55 (3): 938-947. 1990.
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15On the ultrafilters and ultrapowers of strong partition cardinalsJournal of Symbolic Logic 49 (4): 1268-1272. 1984.
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11On the Compactness of $mathbf{aleph}1$ and $mathbf{aleph}2$Journal of Symbolic Logic 43 (3): 394-401. 1978.
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Filter spaces: towards a unified theory of large cardinal and embedding axioms BEIGEL, R., GASARCH, W. and OWINGS, J., Nondeterministic bounded query reducibilities (review)Annals of Pure and Applied Logic 41 299. 1989.
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9Second-order Non-nonstandard AnalysisStudia Logica 74 (3): 399-426. 2003.Following [3], we build higher-order models of analysis resembling the frameworks of nonstandard analysis. The models are entirely canonical, constructed without Choice. Weak transfer principles are developed and the models are applied to topology, graph theory, and measure theory. A Loeb-like measure is constructed.