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On the minimal cover property and certain notions of finite

Eleftherios Tachtsis

Archive for Mathematical Logic 57 (5-6):665-686 (2018)

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The structure of amorphous sets.J. K. Truss - 1995 - Annals of Pure and Applied Logic 73 (2):191-233.details A set is said to be amorphous if it is infinite, but is not the disjoint union of two infinite subsets. Thus amorphous sets can exist only if the axiom of choice is false. We give a general study of the structure which an amorphous set can carry, with the object of eventually obtaining a complete classification. The principal types of amorphous set we distinguish are the following: amorphous sets not of projective type, either bounded or unbounded size of members (...) Logic and Philosophy of Logic Model Theory in Logic and Philosophy of Logic Direct download (4 more) Export citation Bookmark 13 citations
On ramsey’s theorem and the existence of infinite chains or infinite anti-chains in infinite posets.Eleftherios Tachtsis - 2016 - Journal of Symbolic Logic 81 (1):384-394.details Logic and Philosophy of Logic Direct download (3 more) Export citation Bookmark 6 citations
Zermelo-Fraenkel consistency results by Fraenkel-Mostowski methods.David Pincus - 1972 - Journal of Symbolic Logic 37 (4):721-743.details Logic and Philosophy of Logic Logic and Philosophy of Logic, Miscellaneous in Logic and Philosophy of Logic Polish Philosophy in European Philosophy Direct download (7 more) Export citation Bookmark 27 citations
Adding dependent choice.David Pincus - 1977 - Annals of Mathematical Logic 11 (1):105.details Logic and Philosophy of Logic Direct download (3 more) Export citation Bookmark 15 citations
The strength of the $\Delta$-system lemma.Paul Howard & Jeffrey Solski - 1992 - Notre Dame Journal of Formal Logic 34 (1):100-106.details Logic and Philosophy of Logic Logic and Philosophy of Logic, Miscellaneous in Logic and Philosophy of Logic Logics in Logic and Philosophy of Logic Model Theory in Logic and Philosophy of Logic Direct download (5 more) Export citation Bookmark 3 citations
On the set-theoretic strength of the existence of disjoint cofinal sets in posets without maximal elements.Paul Howard, Denis I. Saveliev & Eleftherios Tachtsis - 2016 - Mathematical Logic Quarterly 62 (3):155-176.details In set theory without the Axiom of Choice math formula, we study the deductive strength of the statements math formula, math formula, math formula, and math formula. Among various results, we prove that none of the above statements is provable without using some form of choice, math formula is equivalent to math formula, math formula + math formula implies math formula, math formula does not imply math formula in math formula, math formula does not imply math formula in math formula (...) No categories Direct download (2 more) Export citation Bookmark 3 citations
Well Ordered Subsets of Linearly Ordered Sets.Hartmut Höft & Paul Howard - 1994 - Notre Dame Journal of Formal Logic 35 (3):413-425.details The deductive relationships between six statements are examined in set theory without the axiom of choice. Each of these statements follows from the axiom of choice and involves linear orderings in some way. Logic and Philosophy of Logic Logic and Philosophy of Logic, Miscellaneous in Logic and Philosophy of Logic Model Theory in Logic and Philosophy of Logic Direct download (6 more) Export citation Bookmark 1 citation
Ramsey's theorem in the hierarchy of choice principles.Andreas Blass - 1977 - Journal of Symbolic Logic 42 (3):387-390.details Logic and Philosophy of Logic Logic and Philosophy of Logic, Miscellaneous in Logic and Philosophy of Logic Direct download (7 more) Export citation Bookmark 12 citations

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