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  1. Terminal Notions in Set Theory.Jindřich Zapletal - 2001 - Annals of Pure and Applied Logic 109 (1-2):89-116.
    In mathematical practice certain formulas φ are believed to essentially decide all other natural properties of the object x. The purpose of this paper is to exactly quantify such a belief for four formulas φ, namely “x is a Ramsey ultrafilter”, “x is a free Souslin tree”, “x is an extendible strong Lusin set” and “x is a good diamond sequence”.
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  • Canonical Models for ℵ1-Combinatorics.Saharon Shelah & Jindr̆ich Zapletal - 1999 - Annals of Pure and Applied Logic 98 (1-3):217-259.
    We define the property of Π2-compactness of a statement Φ of set theory, meaning roughly that the hard core of the impact of Φ on combinatorics of 1 can be isolated in a canonical model for the statement Φ. We show that the following statements are Π2-compact: “dominating NUMBER = 1,” “cofinality of the meager IDEAL = 1”, “cofinality of the null IDEAL = 1”, “bounding NUMBER = 1”, existence of various types of Souslin trees and variations on uniformity of (...)
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  • Coding by Club-Sequences.David Asperó - 2006 - Annals of Pure and Applied Logic 142 (1):98-114.
    Given any subset A of ω1 there is a proper partial order which forces that the predicate xA and the predicate xω1A can be expressed by -provably incompatible Σ3 formulas over the structure Hω2,,NSω1. Also, if there is an inaccessible cardinal, then there is a proper partial order which forces the existence of a well-order of Hω2 definable over Hω2,,NSω1 by a provably antisymmetric Σ3 formula with two free variables. The proofs of these results involve a technique for manipulating the (...)
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  • Chain Homogeneous Souslin Algebras.Gido Scharfenberger-Fabian - 2011 - Mathematical Logic Quarterly 57 (6):591-610.
    Assuming Jensen's principle ◊+ we construct Souslin algebras all of whose maximal chains are pairwise isomorphic as total orders, thereby answering questions of Koppelberg and Todorčević.
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  • Characterizing All Models in Infinite Cardinalities.Lauri Keskinen - 2013 - Annals of Pure and Applied Logic 164 (3):230-250.
    Fix a cardinal κ. We can ask the question: what kind of a logic L is needed to characterize all models of cardinality κ up to isomorphism by their L-theories? In other words: for which logics L it is true that if any models A and B of cardinality κ satisfy the same L-theory then they are isomorphic?It is always possible to characterize models of cardinality κ by their Lκ+,κ+-theories, but we are interested in finding a “small” logic L, i.e., (...)
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