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  1.  1
    On the Consistency Strength of Level by Level Inequivalence.Arthur W. Apter - 2017 - Archive for Mathematical Logic 56 (7-8):715-723.
    We show that the theories “ZFC \ There is a supercompact cardinal” and “ZFC \ There is a supercompact cardinal \ Level by level inequivalence between strong compactness and supercompactness holds” are equiconsistent.
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  2. Adding Many Baumgartner Clubs.David Asperó - 2017 - Archive for Mathematical Logic 56 (7-8):797-810.
    I define a homogeneous \–c.c. proper product forcing for adding many clubs of \ with finite conditions. I use this forcing to build models of \=\aleph _2\), together with \\) and \ large and with very strong failures of club guessing at \.
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  3.  2
    Retracted Article: A Completeness Theorem for Continuous Predicate Modal Logic.Stefano Baratella - 2017 - Archive for Mathematical Logic 56 (7-8):1135-1135.
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  4. Topological Ramsey Spaces From Fraïssé Classes, Ramsey-Classification Theorems, and Initial Structures in the Tukey Types of P-Points.Natasha Dobrinen, José G. Mijares & Timothy Trujillo - 2017 - Archive for Mathematical Logic 56 (7-8):733-782.
    A general method for constructing a new class of topological Ramsey spaces is presented. Members of such spaces are infinite sequences of products of Fraïssé classes of finite relational structures satisfying the Ramsey property. The Product Ramsey Theorem of Sokič is extended to equivalence relations for finite products of structures from Fraïssé classes of finite relational structures satisfying the Ramsey property and the Order-Prescribed Free Amalgamation Property. This is essential to proving Ramsey-classification theorems for equivalence relations on fronts, generalizing the (...)
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  5.  1
    Creature Forcing and Five Cardinal Characteristics in Cichoń’s Diagram.Arthur Fischer, Martin Goldstern, Jakob Kellner & Saharon Shelah - 2017 - Archive for Mathematical Logic 56 (7-8):1045-1103.
    We use a creature construction to show that consistently $$\begin{aligned} \mathfrak d=\aleph _1= {{\mathrm{cov}}}< {{\mathrm{non}}}< {{\mathrm{non}}}< {{\mathrm{cof}}} < 2^{\aleph _0}. \end{aligned}$$The same method shows the consistency of $$\begin{aligned} \mathfrak d=\aleph _1= {{\mathrm{cov}}}< {{\mathrm{non}}}< {{\mathrm{non}}}< {{\mathrm{cof}}} < 2^{\aleph _0}. \end{aligned}$$.
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  6.  1
    Strong Measure Zero and Infinite Games.Fred Galvin, Jan Mycielski & Robert M. Solovay - 2017 - Archive for Mathematical Logic 56 (7-8):725-732.
    We show that strong measure zero sets -totally bounded metric space) can be characterized by the nonexistence of a winning strategy in a certain infinite game. We use this characterization to give a proof of the well known fact, originally conjectured by K. Prikry, that every dense \ subset of the real line contains a translate of every strong measure zero set. We also derive a related result which answers a question of J. Fickett.
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  7.  1
    Strongly Uplifting Cardinals and the Boldface Resurrection Axioms.Joel David Hamkins & Thomas A. Johnstone - 2017 - Archive for Mathematical Logic 56 (7-8):1115-1133.
    We introduce the strongly uplifting cardinals, which are equivalently characterized, we prove, as the superstrongly unfoldable cardinals and also as the almost-hugely unfoldable cardinals, and we show that their existence is equiconsistent over ZFC with natural instances of the boldface resurrection axiom, such as the boldface resurrection axiom for proper forcing.
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  8. Katětov Order on Borel Ideals.Michael Hrušák - 2017 - Archive for Mathematical Logic 56 (7-8):831-847.
    We study the Katětov order on Borel ideals. We prove two structural theorems, one for Borel ideals, the other for analytic P-ideals. We isolate nine important Borel ideals and study the Katětov order among them. We also present a list of fundamental open problems concerning the Katětov order on Borel ideals.
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  9. On Constructions with 2-Cardinals.Piotr Koszmider - 2017 - Archive for Mathematical Logic 56 (7-8):849-876.
    We propose developing the theory of consequences of morasses relevant in mathematical applications in the language alternative to the usual one, replacing commonly used structures by families of sets originating with Velleman’s neat simplified morasses called 2-cardinals. The theory of related trees, gaps, colorings of pairs and forcing notions is reformulated and sketched from a unifying point of view with the focus on the applicability to constructions of mathematical structures like Boolean algebras, Banach spaces or compact spaces. The paper is (...)
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  10. Equimorphy: The Case of Chains.C. Laflamme, M. Pouzet & R. Woodrow - 2017 - Archive for Mathematical Logic 56 (7-8):811-829.
    Two structures are said to be equimorphic if each embeds in the other. Such structures cannot be expected to be isomorphic, and in this paper we investigate the special case of linear orders, here also called chains. In particular we provide structure results for chains having less than continuum many isomorphism classes of equimorphic chains. We deduce as a corollary that any chain has either a single isomorphism class of equimorphic chains or infinitely many.
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  11.  1
    In Memoriam: James Earl Baumgartner.J. A. Larson - 2017 - Archive for Mathematical Logic 56 (7-8):877-909.
    James Earl Baumgartner came of age mathematically during the emergence of forcing as a fundamental technique of set theory, and his seminal research changed the way set theory is done. He made fundamental contributions to the development of forcing, to our understanding of uncountable orders, to the partition calculus, and to large cardinals and their ideals. He promulgated the use of logic such as absoluteness and elementary submodels to solve problems in set theory, he applied his knowledge of set theory (...)
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  12. The Nonstationary Ideal on P_kappa for Lambda Singular.Pierre Matet & Saharon Shelah - 2017 - Archive for Mathematical Logic 56 (7-8):911-934.
    We give a new characterization of the nonstationary ideal on \\) in the case when \ is a regular uncountable cardinal and \ a singular strong limit cardinal of cofinality at least \.
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  13. The Sharp for the Chang Model is Small.William J. Mitchell - 2017 - Archive for Mathematical Logic 56 (7-8):935-982.
    Woodin has shown that if there is a measurable Woodin cardinal then there is, in an appropriate sense, a sharp for the Chang model. We produce, in a weaker sense, a sharp for the Chang model using only the existence of a cardinal \ having an extender of length \.
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  14. Codings and Strongly Inaccessible Cardinals.Tadatoshi Miyamoto - 2017 - Archive for Mathematical Logic 56 (7-8):1037-1044.
    We show that a coding principle introduced by J. Moore with respect to all ladder systems is equiconsistent with the existence of a strongly inaccessible cardinal. We also show that a coding principle introduced by S. Todorcevic has consistency strength at least of a strongly inaccessible cardinal.
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  15. Baumgartner’s Isomorphism Problem for $$Aleph _2$$ ℵ 2 -Dense Suborders of $$Mathbb {R}$$ R.Justin Tatch Moore & Stevo Todorcevic - 2017 - Archive for Mathematical Logic 56 (7-8):1105-1114.
    In this paper we will analyze Baumgartner’s problem asking whether it is consistent that \ and every pair of \-dense subsets of \ are isomorphic as linear orders. The main result is the isolation of a combinatorial principle \\) which is immune to c.c.c. forcing and which in the presence of \ implies that two \-dense sets of reals can be forced to be isomorphic via a c.c.c. poset. Also, it will be shown that it is relatively consistent with ZFC (...)
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  16. Two Applications of Finite Side Conditions at Omega _2.Itay Neeman - 2017 - Archive for Mathematical Logic 56 (7-8):983-1036.
    We present two applications of forcing with finite sequences of models as side conditions, adding objects of size \. The first involves adding a \ sequence and variants of such sequences. The second involves adding partial weak specializing functions for trees of height \.
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  17.  2
    Same Graph, Different Universe.Assaf Rinot - 2017 - Archive for Mathematical Logic 56 (7-8):783-796.
    May the same graph admit two different chromatic numbers in two different universes? How about infinitely many different values? and can this be achieved without changing the cardinals structure? In this paper, it is proved that in Gödel’s constructible universe, for every uncountable cardinal \ below the first fixed-point of the \-function, there exists a graph \ satisfying the following:\ has size and chromatic number \;for every infinite cardinal \, there exists a cofinality-preserving \-preserving forcing extension in which \=\kappa \).
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  18.  1
    Bounded Low and High Sets.Bernard A. Anderson, Barbara F. Csima & Karen M. Lange - 2017 - Archive for Mathematical Logic 56 (5-6):507-521.
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  19. A Predicate Extension of Real Valued Logic.Stefano Baratella - 2017 - Archive for Mathematical Logic 56 (5-6):585-605.
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  20.  1
    Uniform Proofs of ACC Representations.Buss Sam - 2017 - Archive for Mathematical Logic 56 (5-6):639-669.
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  21.  1
    A Herbrandized Functional Interpretation of Classical First-Order Logic.Fernando Ferreira & Gilda Ferreira - 2017 - Archive for Mathematical Logic 56 (5-6):523-539.
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  22. A Null Ideal for Inaccessibles.Sy-David Friedman & Giorgio Laguzzi - 2017 - Archive for Mathematical Logic 56 (5-6):691-697.
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  23.  1
    Interpretability Suprema in Peano Arithmetic.Paula Henk & Albert Visser - 2017 - Archive for Mathematical Logic 56 (5-6):555-584.
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  24. A Logic for Arguing About Probabilities in Measure Teams.Tapani Hyttinen, Gianluca Paolini & Jouko Väänänen - 2017 - Archive for Mathematical Logic 56 (5-6):475-489.
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  25.  1
    The Reverse Mathematics of Non-Decreasing Subsequences.Patey Ludovic - 2017 - Archive for Mathematical Logic 56 (5-6):491-506.
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  26. Ordinal Notation Systems Corresponding to Friedman’s Linearized Well-Partial-Orders with Gap-Condition.Michael Rathjen, Jeroen Van der Meeren & Andreas Weiermann - 2017 - Archive for Mathematical Logic 56 (5-6):607-638.
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  27.  1
    Minimal Elementary End Extensions.James H. Schmerl - 2017 - Archive for Mathematical Logic 56 (5-6):541-553.
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  28. The Strength of Countable Saturation.Benno van den Berg, Eyvind Briseid & Pavol Safarik - 2017 - Archive for Mathematical Logic 56 (5-6):699-711.
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  29. Saturation and Solvability in Abstract Elementary Classes with Amalgamation.Sebastien Vasey - 2017 - Archive for Mathematical Logic 56 (5-6):671-690.
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  30.  3
    Models of Weak Theories of Truth.Mateusz Łełyk & Bartosz Wcisło - 2017 - Archive for Mathematical Logic 56 (5-6):453-474.
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  31. The Countable Existentially Closed Pseudocomplemented Semilattice.Joël Adler - 2017 - Archive for Mathematical Logic 56 (3-4):397-402.
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  32. Chains of Saturated Models in AECs.Will Boney & Sebastien Vasey - 2017 - Archive for Mathematical Logic 56 (3-4):187-213.
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  33. A Strong Partition Cardinal Above $$\varTheta $$ Θ.Daniel W. Cunningham - 2017 - Archive for Mathematical Logic 56 (3-4):403-421.
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  34. An Easton Like Theorem in the Presence of Shelah Cardinals.Mohammad Golshani - 2017 - Archive for Mathematical Logic 56 (3-4):273-287.
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  35. Magidor–Malitz Reflection.Yair Hayut - 2017 - Archive for Mathematical Logic 56 (3-4):253-272.
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  36.  1
    A Generalized Borel-Reducibility Counterpart of Shelah’s Main Gap Theorem.Tapani Hyttinen, Vadim Kulikov & Miguel Moreno - 2017 - Archive for Mathematical Logic 56 (3-4):175-185.
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  37. The Complexity of Topological Conjugacy of Pointed Cantor Minimal Systems.Burak Kaya - 2017 - Archive for Mathematical Logic 56 (3-4):215-235.
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  38.  3
    Coherent Trees That Are Not Countryman.Yinhe Peng - 2017 - Archive for Mathematical Logic 56 (3-4):237-251.
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  39. The Complexity of Isomorphism for Complete Theories of Linear Orders with Unary Predicates.Richard Rast - 2017 - Archive for Mathematical Logic 56 (3-4):289-307.
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  40. Reverse Mathematics and Order Theoretic Fixed Point Theorems.Takashi Sato & Takeshi Yamazaki - 2017 - Archive for Mathematical Logic 56 (3-4):385-396.
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  41. A Parallel to the Null Ideal for Inaccessible $$\Lambda $$ Λ : Part I.Saharon Shelah - 2017 - Archive for Mathematical Logic 56 (3-4):319-383.
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  42. Some Definable Properties of Sets in Non-Valuational Weakly o-Minimal Structures.Somayyeh Tari - 2017 - Archive for Mathematical Logic 56 (3-4):309-317.
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  43. Symmetry in Abstract Elementary Classes with Amalgamation.Monica M. VanDieren & Sebastien Vasey - 2017 - Archive for Mathematical Logic 56 (3-4):423-452.
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  44. Generic Vopěnka’s Principle, Remarkable Cardinals, and the Weak Proper Forcing Axiom.Joan Bagaria, Victoria Gitman & Ralf Schindler - 2017 - Archive for Mathematical Logic 56 (1-2):1-20.
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  45. Definable Types in the Theory of Closed Ordered Differential Fields.Quentin Brouette - 2017 - Archive for Mathematical Logic 56 (1-2):119-129.
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  46. MV-Algebras, Infinite Dimensional Polyhedra, and Natural Dualities.Leonardo M. Cabrer & Luca Spada - 2017 - Archive for Mathematical Logic 56 (1-2):21-42.
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  47. Relations Between the $${\Mathcal {I}}$$ I -Ultrafilters.Hong Jianyong & Zhang Shuguo - 2017 - Archive for Mathematical Logic 56 (1-2):161-173.
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  48. Computable Ramsey’s Theorem for Pairs Needs Infinitely Many $$\Pi ^0_2$$ Π 2 0 Sets.Gregory Igusa & Henry Towsner - 2017 - Archive for Mathematical Logic 56 (1-2):155-160.
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  49. Locally Compact Groups Which Are Separably Categorical Structures.Aleksander Ivanov - 2017 - Archive for Mathematical Logic 56 (1-2):67-78.
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  50. An Induction Principle Over Real Numbers.A. Mahboubi - 2017 - Archive for Mathematical Logic 56 (1-2):43-49.
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  51. Constructions of Categories of Setoids From Proof-Irrelevant Families.Erik Palmgren - 2017 - Archive for Mathematical Logic 56 (1-2):51-66.
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  52. $$I_0$$ I 0 and Combinatorics at $$\Lambda ^+$$ Λ +.Shi Xianghui & Trang Nam - 2017 - Archive for Mathematical Logic 56 (1-2):131-154.
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  53. An Order-Theoretic Characterization of the Howard–Bachmann-Hierarchy.Jeroen Van der Meeren, Michael Rathjen & Andreas Weiermann - 2017 - Archive for Mathematical Logic 56 (1-2):79-118.
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