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Games with creatures

Saharon Shelah, Jindřich Zapletal (2003)

Commentationes Mathematicae Universitatis Carolinae

Many forcing notions obtained using the creature technology are naturally connected with certain integer games.

Generic extensions of models of ZFC

Lev Bukovský (2017)

Commentationes Mathematicae Universitatis Carolinae

The paper contains a self-contained alternative proof of my Theorem in Characterization of generic extensions of models of set theory, Fund. Math. 83 (1973), 35–46, saying that for models M N of ZFC with same ordinals, the condition A p r M , N ( κ ) implies that N is a κ -C.C. generic extension of M .

Goldstern–Judah–Shelah preservation theorem for countable support iterations

Miroslav Repický (1994)

Fundamenta Mathematicae

[1] T. Bartoszyński, Additivity of measure implies additivity of category, Trans. Amer. Math. Soc. 281 (1984), 209-213. [2] T. Bartoszyński and H. Judah, Measure and Category, in preparation. [3] D. H. Fremlin, Cichoń’s diagram, Publ. Math. Univ. Pierre Marie Curie 66, Sém. Initiation Anal., 1983/84, Exp. 5, 13 pp. [4] M. Goldstern, Tools for your forcing construction, in: Set Theory of the Reals, Conference of Bar-Ilan University, H. Judah (ed.), Israel Math. Conf. Proc. 6, 1992, 307-362. [5] H....

Guessing clubs in the generalized club filter

Bernhard König, Paul Larson, Yasuo Yoshinobu (2007)

Fundamenta Mathematicae

We present principles for guessing clubs in the generalized club filter on κ λ . These principles are shown to be weaker than classical diamond principles but often serve as sufficient substitutes. One application is a new construction of a λ⁺-Suslin-tree using assumptions different from previous constructions. The other application partly solves open problems regarding the cofinality of reflection points for stationary subsets of [ λ ] .

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