Archives
Keywords
Diamond-sharp Intersection model 54G20 Strongly compact cardinal Fast club tensor product graph higher Baire space Greatly Mahlo Dowker space Singular Density Luzin set Ineffable cardinal Diamond square Almost Souslin Knaster and friends Sierpinski's onto mapping principle incompactness Axiom R Subtle tree property diamond star Cohen real Iterated forcing Commutative cancellative semigroups club_AD Commutative projection system Rainbow sets Martin's Axiom Sakurai's Bell inequality Kurepa Hypothesis Uniformly homogeneous Distributive tree Slim tree Prevalent singular cardinals Generalized Clubs Singular cofinality stationary hitting Nonspecial tree Parameterized proxy principle Cardinal function Whitehead Problem L-space Souslin Tree Singular cardinals combinatorics Generalized descriptive set theory sap reflection principles OCA Cardinal Invariants square principles Precaliber Almost-disjoint family Large Cardinals regressive Souslin tree Chang's conjecture Shelah's Strong Hypothesis Knaster Non-saturation Local Club Condensation. Minimal Walks Strongly Luzin set Ramsey theory over partitions Analytic sets Ascent Path transformations Postprocessing function Subadditive stick Prikry-type forcing Aronszajn tree Erdos Cardinal Coherent tree SNR weak Kurepa tree Selective Ultrafilter strongly bounded groups Universal Sequences polarized partition relation Constructible Universe PFA Was Ulam right? Sigma-Prikry ccc Antichain Hereditarily Lindelöf space unbounded function Rado's conjecture Square-Brackets Partition Relations Club Guessing Lipschitz reduction Dushnik-Miller free Souslin tree indecomposable ultrafilter Reflecting stationary set nonmeager set Fodor-type reflection specializable Souslin tree P-Ideal Dichotomy positive partition relation full tree C-sequence Uniformly coherent middle diamond Ulam matrix Jonsson cardinal Open Access Poset coloring number Well-behaved magma GMA O-space approachability ideal countably metacompact Strong coloring Partition Relations xbox Amenable C-sequence weak square S-Space Hedetniemi's conjecture Countryman line Forcing Axioms Chromatic number Weakly compact cardinal projective Boolean algebra Respecting tree Almost countably chromatic weak diamond Subtle cardinal AIM forcing Microscopic Approach b-scale Uniformization Reduced Power very good scale stationary reflection Small forcing Forcing Filter reflection Rock n' Roll Erdos-Hajnal graphs HOD Fat stationary set Subnormal ideal Successor of Singular Cardinal Mandelbrot set super-Souslin tree Diamond for trees free Boolean algebra Hindman's Theorem ZFC construction Ostaszewski square PFA(S)[S] Successor of Regular Cardinal Vanishing levels Foundations Closed coloring Absoluteness
Author Archives: Assaf Rinot
A new model for all C-sequences are trivial
Joint work with Zhixing You and Jiachen Yuan. Abstract. We construct a model in which all C-sequences are trivial, yet there exists a
Posted in Compactness, Preprints
Tagged Ascent Path, C-sequence, Intersection model, Souslin Tree, Vanishing levels
Comments Off on A new model for all C-sequences are trivial
MFO workshop in Set Theory, January 2025
I gave an invited talk at the Set Theory meeting in Obwerwolfach, January 2025. Talk Title: Non-structure theorems for higher Aronszajn lines. Abstract: An
Posted in Invited Talks
Tagged Countryman line
Comments Off on MFO workshop in Set Theory, January 2025
Walks on uncountable ordinals and non-structure theorems for higher Aronszajn lines
Joint work with Tanmay Inamdar. Abstract. We investigate global structural properties of linear orders of a fixed infinite size. It is classical that the countable linear orders and the continuum-sized orders exhibit contrasting behaviours. Modern results show that strong extensions … Continue reading
Ketonen’s question and other cardinal sins
Joint work with Zhixing You and Jiachen Yuan. Abstract. Intersection models of generic extensions obtained from a commutative projection systems of notions of forcing has recently regained interest, especially in the study of descriptive set theory. Here, we show that … Continue reading
Posted in Compactness, Preprints
Tagged 03E05, 03E35, 03E55, Ascent Path, C-sequence, Commutative projection system, indecomposable ultrafilter, Intersection model, Strongly compact cardinal
Comments Off on Ketonen’s question and other cardinal sins
120 Years of Choice, July 2024
I gave an invited talk at the 120 Years of Choice conference, July 2024. Talk Title: Mathematician’s best friend Abstract: Jensen’s diamond is a very useful postulate. It is well-known that it implies the continuum hypothesis, that it is equivalent … Continue reading
Diamond on Kurepa trees
Joint work with Ziemek Kostana and Saharon Shelah. Abstract. We introduce a new weak variation of diamond that is meant to only guess the branches of a Kurepa tree. We demonstrate that this variation is considerably weaker than diamond by … Continue reading
Posted in Preprints, Squares and Diamonds
Tagged Diamond, Diamond for trees, Iterated forcing, Kurepa Hypothesis, weak Kurepa tree
1 Comment
Proxy principles in combinatorial set theory
Joint work with Ari Meir Brodsky and Shira Yadai. Abstract. The parameterized proxy principles were introduced by Brodsky and Rinot in a 2017 paper as new foundations for the construction of
Squares, ultrafilters and forcing axioms
Joint work with Chris Lambie-Hanson and Jing Zhang. Abstract. We study the interplay of the three families of combinatorial objects or principles. Specifically, we show the following. Strong forcing axioms, in general incompatible with the existence of indexed squares, can … Continue reading
Posted in Compactness, Preprints
Tagged Forcing Axioms, indecomposable ultrafilter, Subadditive, unbounded function
Comments Off on Squares, ultrafilters and forcing axioms
May the successor of a singular cardinal be Jonsson?
Abstract: We collect necessary conditions for the successor of a singular cardinal to be Jónsson.
Posted in Open Problems, Singular Cardinals Combinatorics
Tagged Jonsson cardinal
Comments Off on May the successor of a singular cardinal be Jonsson?
