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There may be simple Paleph1 and Paleph2-points and the Rudin-Keisler ordering may be downward directed.

, and . Ann. Pure Appl. Log., (1987)

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Seven trees in one. J. Pure Appl. Algebra, 103 (1): 1--21 (1995)The Underlying Logic of Hoare Logic., and . Bulletin of the EATCS, (2000)Algorithms vs. Machines., and . Bulletin of the EATCS, (2002)A Variation on the Zero-One Law., , , and . Inf. Process. Lett., 67 (1): 29-30 (1998)The Model of Set Theory Generated by Countably Many Generic Reals.. J. Symb. Log., 46 (4): 732-752 (1981)The Intersection of Nonstandard Models of Arithmetic.. J. Symb. Log., 37 (1): 103-106 (1972)Amalgamation of Nonstandard Models of Arithmetic.. J. Symb. Log., 42 (3): 372-386 (1977)On Certain Types and Models for Arithmetic.. J. Symb. Log., 39 (1): 151-162 (1974)Groupwise density and related cardinals.. Arch. Math. Log., 30 (1): 1-11 (1990)Infinitary Combinatorics and Modal Logic.. J. Symb. Log., 55 (2): 761-778 (1990)